diff --git a/Documentation/packaging.md b/Documentation/packaging.md
index 6d0d6d95e..a049a8102 100644
--- a/Documentation/packaging.md
+++ b/Documentation/packaging.md
@@ -43,7 +43,7 @@ Follow the directions within https://packaging.python.org/tutorials/packaging-pr
Deactivate the virtualenv, and make or use a different Python 2.7 virtualenv to test that you can `pip install` the `sdist` you've just made. One thing you can do to quickly verify that the package installs OK:
`>>> import HARK.simulation`
-`>>> HARK.simulation.drawBernoulli(5)`
+`>>> HARK.simulation.Bernoulli().draw(5)`
You should get something like:
diff --git a/HARK/ConsumptionSaving/ConsAggShockModel.py b/HARK/ConsumptionSaving/ConsAggShockModel.py
index d30a2d08b..d5b99ea65 100644
--- a/HARK/ConsumptionSaving/ConsAggShockModel.py
+++ b/HARK/ConsumptionSaving/ConsAggShockModel.py
@@ -15,7 +15,7 @@
VariableLowerBoundFunc2D, BilinearInterp, LowerEnvelope2D, UpperEnvelope
from HARK.utilities import CRRAutility, CRRAutilityP, CRRAutilityPP, CRRAutilityP_inv,\
CRRAutility_invP, CRRAutility_inv
-from HARK.simulation import drawUniform
+from HARK.distribution import Uniform
from HARK.ConsumptionSaving.ConsIndShockModel import ConsumerSolution, IndShockConsumerType, init_idiosyncratic_shocks
from HARK import HARKobject, Market, AgentType
from copy import deepcopy
@@ -89,7 +89,7 @@ class AggShockConsumerType(IndShockConsumerType):
evolves over time and take aggregate shocks into account when making their
decision about how much to consume.
'''
- def __init__(self, time_flow=True, **kwds):
+ def __init__(self, **kwds):
'''
Make a new instance of AggShockConsumerType, an extension of
IndShockConsumerType. Sets appropriate solver and input lists.
@@ -98,7 +98,7 @@ def __init__(self, time_flow=True, **kwds):
params.update(kwds)
AgentType.__init__(self, solution_terminal=deepcopy(IndShockConsumerType.solution_terminal_),
- time_flow=time_flow, pseudo_terminal=False, **params)
+ pseudo_terminal=False, **params)
# Add consumer-type specific objects, copying to create independent versions
self.time_vary = deepcopy(IndShockConsumerType.time_vary_)
@@ -1629,7 +1629,7 @@ def makeMrkvHist(self):
# Add histories until each state has been visited at least state_T_min times
while go:
- draws = drawUniform(N=self.act_T_orig, seed=loops)
+ draws = Uniform().draw(N=self.act_T_orig, seed=loops)
for s in range(draws.size): # Add act_T_orig more periods
MrkvNow_hist[t] = MrkvNow
MrkvNow = np.searchsorted(cutoffs[MrkvNow, :], draws[s])
diff --git a/HARK/ConsumptionSaving/ConsGenIncProcessModel.py b/HARK/ConsumptionSaving/ConsGenIncProcessModel.py
index 8af0ec76e..8efb71143 100644
--- a/HARK/ConsumptionSaving/ConsGenIncProcessModel.py
+++ b/HARK/ConsumptionSaving/ConsGenIncProcessModel.py
@@ -17,7 +17,7 @@
from HARK.utilities import CRRAutility, CRRAutilityP, CRRAutilityPP, CRRAutilityP_inv, \
CRRAutility_invP, CRRAutility_inv, CRRAutilityP_invP,\
getPercentiles
-from HARK.simulation import drawLognormal, drawUniform
+from HARK.distribution import Lognormal, Uniform
from HARK.ConsumptionSaving.ConsIndShockModel import ConsIndShockSetup, ConsumerSolution, IndShockConsumerType, init_idiosyncratic_shocks
__all__ = ['ValueFunc2D', 'MargValueFunc2D', 'MargMargValueFunc2D', 'pLvlFuncAR1',
@@ -985,7 +985,7 @@ class GenIncProcessConsumerType(IndShockConsumerType):
solution_terminal_ = ConsumerSolution(cFunc=cFunc_terminal_, mNrmMin=0.0, hNrm=0.0, MPCmin=1.0, MPCmax=1.0)
poststate_vars_ = ['aLvlNow', 'pLvlNow']
- def __init__(self, cycles=0, time_flow=True, **kwds):
+ def __init__(self, cycles=0, **kwds):
'''
Instantiate a new ConsumerType with given data.
See ConsumerParameters.init_explicit_perm_inc for a dictionary of the
@@ -995,8 +995,6 @@ def __init__(self, cycles=0, time_flow=True, **kwds):
----------
cycles : int
Number of times the sequence of periods should be solved.
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
Returns
-------
@@ -1006,7 +1004,7 @@ def __init__(self, cycles=0, time_flow=True, **kwds):
params.update(kwds)
# Initialize a basic ConsumerType
- IndShockConsumerType.__init__(self, cycles=cycles, time_flow=time_flow, **params)
+ IndShockConsumerType.__init__(self, cycles=cycles, **params)
self.solveOnePeriod = solveConsGenIncProcess # idiosyncratic shocks solver with explicit persistent income
def preSolve(self):
@@ -1109,13 +1107,12 @@ def updatepLvlGrid(self):
-------
None
'''
- orig_time = self.time_flow
- self.timeFwd()
LivPrbAll = np.array(self.LivPrb)
# Simulate the distribution of persistent income levels by t_cycle in a lifecycle model
if self.cycles == 1:
- pLvlNow = drawLognormal(self.AgentCount, mu=self.pLvlInitMean, sigma=self.pLvlInitStd, seed=31382)
+ pLvlNow = Lognormal(self.pLvlInitMean,
+ sigma=self.pLvlInitStd,).draw(self.AgentCount, seed=31382)
pLvlGrid = [] # empty list of time-varying persistent income grids
# Calculate distribution of persistent income in each period of lifecycle
for t in range(len(self.PermShkStd)):
@@ -1129,14 +1126,15 @@ def updatepLvlGrid(self):
# Calculate "stationary" distribution in infinite horizon (might vary across periods of cycle)
elif self.cycles == 0:
T_long = 1000 # Number of periods to simulate to get to "stationary" distribution
- pLvlNow = drawLognormal(self.AgentCount, mu=self.pLvlInitMean, sigma=self.pLvlInitStd, seed=31382)
+ pLvlNow = Lognormal(mu=self.pLvlInitMean,
+ sigma=self.pLvlInitStd).draw(self.AgentCount, seed=31382)
t_cycle = np.zeros(self.AgentCount, dtype=int)
for t in range(T_long):
LivPrb = LivPrbAll[t_cycle] # Determine who dies and replace them with newborns
- draws = drawUniform(self.AgentCount, seed=t)
+ draws = Uniform().draw(self.AgentCount, seed=t)
who_dies = draws > LivPrb
- pLvlNow[who_dies] = drawLognormal(np.sum(who_dies), mu=self.pLvlInitMean,
- sigma=self.pLvlInitStd, seed=t+92615)
+ pLvlNow[who_dies] = Lognormal(self.pLvlInitMean,
+ self.pLvlInitStd).draw(np.sum(who_dies), seed=t+92615)
t_cycle[who_dies] = 0
for j in range(self.T_cycle): # Update persistent income
@@ -1161,8 +1159,6 @@ def updatepLvlGrid(self):
# Store the result and add attribute to time_vary
self.pLvlGrid = pLvlGrid
self.addToTimeVary('pLvlGrid')
- if not orig_time:
- self.timeRev()
def simBirth(self, which_agents):
'''
@@ -1181,10 +1177,13 @@ def simBirth(self, which_agents):
'''
# Get and store states for newly born agents
N = np.sum(which_agents) # Number of new consumers to make
- aNrmNow_new = drawLognormal(N, mu=self.aNrmInitMean, sigma=self.aNrmInitStd,
+ aNrmNow_new = Lognormal(self.aNrmInitMean,
+ self.aNrmInitStd).draw(
+ N,
seed=self.RNG.randint(0, 2**31-1))
- self.pLvlNow[which_agents] = drawLognormal(N, mu=self.pLvlInitMean, sigma=self.pLvlInitStd,
- seed=self.RNG.randint(0, 2**31-1))
+ self.pLvlNow[which_agents] = Lognormal(self.pLvlInitMean,
+ self.pLvlInitStd).draw(N,
+ seed=self.RNG.randint(0, 2**31-1))
self.aLvlNow[which_agents] = aNrmNow_new*self.pLvlNow[which_agents]
self.t_age[which_agents] = 0 # How many periods since each agent was born
self.t_cycle[which_agents] = 0 # Which period of the cycle each agent is currently in
@@ -1278,18 +1277,12 @@ def updatepLvlNextFunc(self):
-------
None
'''
- orig_time = self.time_flow
- self.timeFwd()
-
pLvlNextFunc = []
for t in range(self.T_cycle):
pLvlNextFunc.append(LinearInterp(np.array([0., 1.]), np.array([0., self.PermGroFac[t]])))
self.pLvlNextFunc = pLvlNextFunc
self.addToTimeVary('pLvlNextFunc')
- if not orig_time:
- self.timeRev()
-
###############################################################################
@@ -1330,7 +1323,6 @@ def __init__(self, cycles=0, time_flow=True, **kwds):
GenIncProcessConsumerType.__init__(self,
cycles=cycles,
- time_flow=time_flow,
**params)
def updatepLvlNextFunc(self):
@@ -1348,8 +1340,6 @@ def updatepLvlNextFunc(self):
-------
None
'''
- orig_time = self.time_flow
- self.timeFwd()
pLvlNextFunc = []
pLogMean = self.pLvlInitMean # Initial mean (log) persistent income
@@ -1360,5 +1350,3 @@ def updatepLvlNextFunc(self):
self.pLvlNextFunc = pLvlNextFunc
self.addToTimeVary('pLvlNextFunc')
- if not orig_time:
- self.timeRev()
diff --git a/HARK/ConsumptionSaving/ConsIndShockModel.py b/HARK/ConsumptionSaving/ConsIndShockModel.py
index 2849a4201..8a474f720 100644
--- a/HARK/ConsumptionSaving/ConsIndShockModel.py
+++ b/HARK/ConsumptionSaving/ConsIndShockModel.py
@@ -24,7 +24,7 @@
from HARK import AgentType, Solution, NullFunc, HARKobject
from HARK.utilities import warnings # Because of "patch" to warnings modules
from HARK.interpolation import CubicInterp, LowerEnvelope, LinearInterp
-from HARK.simulation import drawLognormal, drawUniform
+from HARK.distribution import Lognormal, Uniform
from HARK.distribution import DiscreteDistribution, approxMeanOneLognormal, addDiscreteOutcomeConstantMean, combineIndepDstns
from HARK.utilities import makeGridExpMult, CRRAutility, CRRAutilityP, \
CRRAutilityPP, CRRAutilityP_inv, CRRAutility_invP, CRRAutility_inv, \
@@ -1621,7 +1621,6 @@ class PerfForesightConsumerType(AgentType):
def __init__(self,
cycles=1,
- time_flow=True,
verbose=False,
quiet=False,
**kwds):
@@ -1634,8 +1633,6 @@ def __init__(self,
----------
cycles : int
Number of times the sequence of periods should be solved.
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
Returns
-------
@@ -1648,7 +1645,8 @@ def __init__(self,
# Initialize a basic AgentType
AgentType.__init__(self,solution_terminal=deepcopy(self.solution_terminal_),
- cycles=cycles,time_flow=time_flow,pseudo_terminal=False,**kwds)
+ cycles=cycles,
+ pseudo_terminal=False,**kwds)
# Add consumer-type specific objects, copying to create independent versions
self.time_vary = deepcopy(self.time_vary_)
@@ -1745,9 +1743,11 @@ def simBirth(self,which_agents):
'''
# Get and store states for newly born agents
N = np.sum(which_agents) # Number of new consumers to make
- self.aNrmNow[which_agents] = drawLognormal(N,mu=self.aNrmInitMean,sigma=self.aNrmInitStd,seed=self.RNG.randint(0,2**31-1))
+ self.aNrmNow[which_agents] = Lognormal(mu=self.aNrmInitMean,
+ sigma=self.aNrmInitStd).draw(N,seed=self.RNG.randint(0,2**31-1))
pLvlInitMeanNow = self.pLvlInitMean + np.log(self.PlvlAggNow) # Account for newer cohorts having higher permanent income
- self.pLvlNow[which_agents] = drawLognormal(N,mu=pLvlInitMeanNow,sigma=self.pLvlInitStd,seed=self.RNG.randint(0,2**31-1))
+ self.pLvlNow[which_agents] = Lognormal(pLvlInitMeanNow,
+ self.pLvlInitStd,).draw(N,seed=self.RNG.randint(0,2**31-1))
self.t_age[which_agents] = 0 # How many periods since each agent was born
self.t_cycle[which_agents] = 0 # Which period of the cycle each agent is currently in
return None
@@ -1769,7 +1769,7 @@ def simDeath(self):
# Determine who dies
DiePrb_by_t_cycle = 1.0 - np.asarray(self.LivPrb)
DiePrb = DiePrb_by_t_cycle[self.t_cycle-1] # Time has already advanced, so look back one
- DeathShks = drawUniform(N=self.AgentCount,seed=self.RNG.randint(0,2**31-1))
+ DeathShks = Uniform().draw(N=self.AgentCount,seed=self.RNG.randint(0,2**31-1))
which_agents = DeathShks < DiePrb
if self.T_age is not None: # Kill agents that have lived for too many periods
too_old = self.t_age >= self.T_age
@@ -2045,7 +2045,6 @@ class IndShockConsumerType(PerfForesightConsumerType):
def __init__(self,
cycles=1,
- time_flow=True,
verbose=False,
quiet=False,
**kwds):
@@ -2072,7 +2071,6 @@ def __init__(self,
# Initialize a basic AgentType
PerfForesightConsumerType.__init__(self,
cycles=cycles,
- time_flow=time_flow,
verbose=verbose,
quiet=quiet,
**params)
@@ -2094,15 +2092,11 @@ def updateIncomeProcess(self):
-----------
none
'''
- original_time = self.time_flow
- self.timeFwd()
IncomeDstn, PermShkDstn, TranShkDstn = constructLognormalIncomeProcessUnemployment(self)
self.IncomeDstn = IncomeDstn
self.PermShkDstn = PermShkDstn
self.TranShkDstn = TranShkDstn
self.addToTimeVary('IncomeDstn','PermShkDstn','TranShkDstn')
- if not original_time:
- self.timeRev()
def updateAssetsGrid(self):
'''
@@ -2558,7 +2552,7 @@ class KinkedRconsumerType(IndShockConsumerType):
time_inv_.remove('Rfree')
time_inv_ += ['Rboro', 'Rsave']
- def __init__(self,cycles=1,time_flow=True,**kwds):
+ def __init__(self,cycles=1,**kwds):
'''
Instantiate a new ConsumerType with given data.
See ConsumerParameters.init_kinked_R for a dictionary of
@@ -2568,8 +2562,6 @@ def __init__(self,cycles=1,time_flow=True,**kwds):
----------
cycles : int
Number of times the sequence of periods should be solved.
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
Returns
-------
@@ -2579,7 +2571,9 @@ def __init__(self,cycles=1,time_flow=True,**kwds):
params.update(kwds)
# Initialize a basic AgentType
- PerfForesightConsumerType.__init__(self,cycles=cycles,time_flow=time_flow,**params)
+ PerfForesightConsumerType.__init__(self,
+ cycles=cycles,
+ **params)
# Add consumer-type specific objects, copying to create independent versions
self.solveOnePeriod = solveConsKinkedR # kinked R solver
@@ -2901,6 +2895,7 @@ def constructAssetsGrid(parameters):
return aXtraGrid
+
# Make a dictionary to specify a lifecycle consumer with a finite horizon
init_lifecycle = copy(init_idiosyncratic_shocks)
init_lifecycle['PermGroFac'] = [1.01,1.01,1.01,1.01,1.01,1.02,1.02,1.02,1.02,1.02]
@@ -2918,4 +2913,3 @@ def constructAssetsGrid(parameters):
init_cyclical['TranShkStd'] = [0.1,0.1,0.1,0.1]
init_cyclical['LivPrb'] = 4*[0.98]
init_cyclical['T_cycle'] = 4
-
diff --git a/HARK/ConsumptionSaving/ConsLaborModel.py b/HARK/ConsumptionSaving/ConsLaborModel.py
index 503cd61d5..2271b5b6f 100644
--- a/HARK/ConsumptionSaving/ConsLaborModel.py
+++ b/HARK/ConsumptionSaving/ConsLaborModel.py
@@ -245,7 +245,7 @@ def solveConsLaborIntMarg(solution_next,PermShkDstn,TranShkDstn,LivPrb,DiscFac,C
class LaborIntMargConsumerType(IndShockConsumerType):
- '''
+ '''
A class representing agents who make a decision each period about how much
to consume vs save and how much labor to supply (as a fraction of their time).
They get CRRA utility from a composite good x_t = c_t*z_t^alpha, and discount
@@ -255,7 +255,7 @@ class LaborIntMargConsumerType(IndShockConsumerType):
time_vary_ += ['WageRte']
time_inv_ = copy(IndShockConsumerType.time_inv_)
- def __init__(self,cycles=1,time_flow=True,**kwds):
+ def __init__(self,cycles=1,**kwds):
'''
Instantiate a new consumer type with given data.
See ConsumerParameters.init_labor_intensive for a dictionary of
@@ -265,8 +265,6 @@ def __init__(self,cycles=1,time_flow=True,**kwds):
----------
cycles : int
Number of times the sequence of periods should be solved.
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
Returns
-------
@@ -275,7 +273,7 @@ def __init__(self,cycles=1,time_flow=True,**kwds):
params = init_labor_intensive.copy()
params.update(kwds)
- IndShockConsumerType.__init__(self,cycles = cycles,time_flow=time_flow,**params)
+ IndShockConsumerType.__init__(self,cycles = cycles,**params)
self.pseudo_terminal = False
self.solveOnePeriod = solveConsLaborIntMarg
self.update()
@@ -318,13 +316,8 @@ def updateLbrCost(self):
for n in range(N):
LbrCostBase += Coeffs[n]*age_vec**n
LbrCost = np.exp(LbrCostBase)
- time_orig = self.time_flow
- self.timeFwd()
self.LbrCost = LbrCost.tolist()
self.addToTimeVary('LbrCost')
- if not time_orig:
- self.timeRev()
-
def calcBoundingValues(self):
'''
@@ -456,18 +449,11 @@ def updateTranShkGrid(self):
-------
None
'''
- time_orig=self.time_flow
- self.timeFwd()
-
TranShkGrid = [] # Create an empty list for TranShkGrid that will be updated
for t in range(self.T_cycle):
TranShkGrid.append(self.TranShkDstn[t][1]) # Update/ Extend the list of TranShkGrid with the TranShkVals for each TranShkPrbs
self.TranShkGrid = TranShkGrid # Save that list in self (time-varying)
self.addToTimeVary('TranShkGrid') # Run the method addToTimeVary from AgentType to add TranShkGrid as one parameter of time_vary list
-
- if not time_orig:
- self.timeRev()
-
def updateSolutionTerminal(self):
'''
@@ -481,11 +467,8 @@ def updateSolutionTerminal(self):
Returns
-------
None
- '''
- if self.time_flow: # To make sure we pick the last element of the list, depending on the direction time is flowing
- t=-1
- else:
- t=0
+ '''
+ t=-1
TranShkGrid = self.TranShkGrid[t]
LbrCost = self.LbrCost[t]
WageRte = self.WageRte[t]
@@ -613,28 +596,3 @@ def plotLbrFunc(self,t,bMin=None,bMax=None,ShkSet=None):
plt.xlabel('Beginning of period bank balances')
plt.ylabel('Labor supply')
plt.show()
-
-
-# Make a default dictionary for the intensive margin labor supply model
-init_labor_intensive = copy(init_idiosyncratic_shocks)
-init_labor_intensive ['LbrCostCoeffs'] = [-1.0]
-init_labor_intensive ['WageRte'] = [1.0]
-init_labor_intensive['IncUnemp'] = 0.0
-init_labor_intensive['TranShkCount'] = 15 # Crank up permanent shock count - Number of points in discrete approximation to transitory income shocks
-init_labor_intensive['PermShkCount'] = 16 # Crank up permanent shock count
-init_labor_intensive ['aXtraCount'] = 200 # May be important to have a larger number of gridpoints (than 48 initially)
-init_labor_intensive ['aXtraMax'] = 80.
-init_labor_intensive ['BoroCnstArt'] = None
-
-# Make a dictionary for intensive margin labor supply model with finite lifecycle
-init_labor_lifecycle = init_labor_intensive.copy()
-init_labor_lifecycle['PermGroFac'] = [1.01,1.01,1.01,1.01,1.01,1.02,1.02,1.02,1.02,1.02]
-init_labor_lifecycle['PermShkStd'] = [0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1]
-init_labor_lifecycle['TranShkStd'] = [0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1]
-init_labor_lifecycle['LivPrb'] = [0.99,0.9,0.8,0.7,0.6,0.5,0.4,0.3,0.2,0.1] # Living probability decreases as time moves forward.
-init_labor_lifecycle['WageRte'] = [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0] # Wage rate in a lifecycle
-init_labor_lifecycle['LbrCostCoeffs'] = [-2.0, 0.4] # Assume labor cost coeffs is a polynomial of degree 1
-init_labor_lifecycle['T_cycle'] = 10
-#init_labor_lifecycle['T_retire'] = 7 # IndexError at line 774 in interpolation.py.
-init_labor_lifecycle['T_age'] = 11 # Make sure that old people die at terminal age and don't turn into newborns!
-
diff --git a/HARK/ConsumptionSaving/ConsMarkovModel.py b/HARK/ConsumptionSaving/ConsMarkovModel.py
index 610e999af..5f57b2804 100644
--- a/HARK/ConsumptionSaving/ConsMarkovModel.py
+++ b/HARK/ConsumptionSaving/ConsMarkovModel.py
@@ -12,8 +12,8 @@
from HARK import AgentType
from HARK.ConsumptionSaving.ConsIndShockModel import ConsIndShockSolver, ValueFunc, \
MargValueFunc, ConsumerSolution, IndShockConsumerType
-from HARK.distribution import DiscreteDistribution
-from HARK.simulation import drawUniform
+
+from HARK.distribution import DiscreteDistribution, Uniform
from HARK.interpolation import CubicInterp, LowerEnvelope, LinearInterp
from HARK.utilities import CRRAutility, CRRAutilityP, CRRAutilityPP, CRRAutilityP_inv, \
CRRAutility_invP, CRRAutility_inv, CRRAutilityP_invP
@@ -683,8 +683,10 @@ class MarkovConsumerType(IndShockConsumerType):
time_vary_ = IndShockConsumerType.time_vary_ + ['MrkvArray']
shock_vars_ = IndShockConsumerType.shock_vars_ + ['MrkvNow']
- def __init__(self,cycles=1,time_flow=True,**kwds):
- IndShockConsumerType.__init__(self,cycles=1,time_flow=True,**kwds)
+ def __init__(self,
+ cycles=1,
+ **kwds):
+ IndShockConsumerType.__init__(self,cycles=1,**kwds)
self.solveOnePeriod = _solveConsMarkov
self.poststate_vars += ['MrkvNow']
if not hasattr(self, 'global_markov'):
@@ -776,7 +778,7 @@ def updateSolutionTerminal(self):
def initializeSim(self):
IndShockConsumerType.initializeSim(self)
if self.global_markov: #Need to initialize markov state to be the same for all agents
- base_draw = drawUniform(1,seed=self.RNG.randint(0,2**31-1))
+ base_draw = Uniform().draw(1,seed=self.RNG.randint(0,2**31-1))
Cutoffs = np.cumsum(np.array(self.MrkvPrbsInit))
self.MrkvNow = np.ones(self.AgentCount)*np.searchsorted(Cutoffs,base_draw).astype(int)
self.MrkvNow = self.MrkvNow.astype(int)
@@ -798,7 +800,7 @@ def simDeath(self):
# Determine who dies
LivPrb = np.array(self.LivPrb)[self.t_cycle-1,self.MrkvNow] # Time has already advanced, so look back one
DiePrb = 1.0 - LivPrb
- DeathShks = drawUniform(N=self.AgentCount,seed=self.RNG.randint(0,2**31-1))
+ DeathShks = Uniform().draw(N=self.AgentCount,seed=self.RNG.randint(0,2**31-1))
which_agents = DeathShks < DiePrb
if self.T_age is not None: # Kill agents that have lived for too many periods
too_old = self.t_age >= self.T_age
@@ -822,7 +824,7 @@ def simBirth(self,which_agents):
IndShockConsumerType.simBirth(self,which_agents) # Get initial assets and permanent income
if not self.global_markov: #Markov state is not changed if it is set at the global level
N = np.sum(which_agents)
- base_draws = drawUniform(N,seed=self.RNG.randint(0,2**31-1))
+ base_draws = Uniform().draw(N,seed=self.RNG.randint(0,2**31-1))
Cutoffs = np.cumsum(np.array(self.MrkvPrbsInit))
self.MrkvNow[which_agents] = np.searchsorted(Cutoffs,base_draws).astype(int)
@@ -842,9 +844,9 @@ def getMarkovStates(self):
'''
# Draw random numbers that will be used to determine the next Markov state
if self.global_markov:
- base_draws = np.ones(self.AgentCount)*drawUniform(1,seed=self.RNG.randint(0,2**31-1))
+ base_draws = np.ones(self.AgentCount)*Uniform().draw(1,seed=self.RNG.randint(0,2**31-1))
else:
- base_draws = drawUniform(self.AgentCount,seed=self.RNG.randint(0,2**31-1))
+ base_draws = Uniform().draw(self.AgentCount,seed=self.RNG.randint(0,2**31-1))
dont_change = self.t_age == 0 # Don't change Markov state for those who were just born (unless global_markov)
if self.t_sim == 0: # Respect initial distribution of Markov states
dont_change[:] = True
@@ -895,13 +897,16 @@ def getShocks(self):
if N > 0:
IncomeDstnNow = self.IncomeDstn[t-1][j] # set current income distribution
PermGroFacNow = self.PermGroFac[t-1][j] # and permanent growth factor
- Indices = np.arange(IncomeDstnNow.pmf.size) # just a list of integers
+
+ Indices = np.arange(IncomeDstnNow[0].size) # just a list of integers
# Get random draws of income shocks from the discrete distribution
- EventDraws = IncomeDstnNow.draw_events(
+ EventDraws = DiscreteDistribution(
+ IncomeDstnNow[0], Indices
+ ).drawDiscrete(
N,
seed=self.RNG.randint(0,2**31-1))
- PermShkNow[these] = IncomeDstnNow.X[0][EventDraws]*PermGroFacNow # permanent "shock" includes expected growth
- TranShkNow[these] = IncomeDstnNow.X[1][EventDraws]
+ PermShkNow[these] = IncomeDstnNow[1][EventDraws]*PermGroFacNow # permanent "shock" includes expected growth
+ TranShkNow[these] = IncomeDstnNow[2][EventDraws]
newborn = self.t_age == 0
PermShkNow[newborn] = 1.0
TranShkNow[newborn] = 1.0
diff --git a/HARK/ConsumptionSaving/ConsMedModel.py b/HARK/ConsumptionSaving/ConsMedModel.py
index 9895f7085..836397f91 100644
--- a/HARK/ConsumptionSaving/ConsMedModel.py
+++ b/HARK/ConsumptionSaving/ConsMedModel.py
@@ -534,7 +534,7 @@ class MedShockConsumerType(PersistentShockConsumerType):
'''
shock_vars_ = PersistentShockConsumerType.shock_vars_ + ['MedShkNow']
- def __init__(self,cycles=0,time_flow=True,**kwds):
+ def __init__(self,cycles=0,**kwds):
'''
Instantiate a new ConsumerType with given data, and construct objects
to be used during solution (income distribution, assets grid, etc).
@@ -545,8 +545,6 @@ def __init__(self,cycles=0,time_flow=True,**kwds):
----------
cycles : int
Number of times the sequence of periods should be solved.
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
Returns
-------
@@ -624,14 +622,9 @@ def updateSolutionTerminal(self):
None
'''
# Take last period data, whichever way time is flowing
- if self.time_flow:
- MedPrice = self.MedPrice[-1]
- MedShkVals = self.MedShkDstn[-1][1]
- MedShkPrbs = self.MedShkDstn[-1][0]
- else:
- MedPrice = self.MedPrice[0]
- MedShkVals = self.MedShkDstn[0][1]
- MedShkPrbs = self.MedShkDstn[0][0]
+ MedPrice = self.MedPrice[-1]
+ MedShkVals = self.MedShkDstn[-1][1]
+ MedShkPrbs = self.MedShkDstn[-1][0]
# Initialize grids of medical need shocks, market resources, and optimal consumption
MedShkGrid = MedShkVals
diff --git a/HARK/ConsumptionSaving/ConsPortfolioModel.py b/HARK/ConsumptionSaving/ConsPortfolioModel.py
index aef9d69e1..7bdbf42da 100644
--- a/HARK/ConsumptionSaving/ConsPortfolioModel.py
+++ b/HARK/ConsumptionSaving/ConsPortfolioModel.py
@@ -23,7 +23,7 @@
MargValueFunc2D # For representing 2D marginal value function
)
from HARK.distribution import approxLognormal, combineIndepDstns
-from HARK.simulation import drawLognormal, drawBernoulli # Random draws for simulating agents
+from HARK.distribution import Lognormal, Bernoulli # Random draws for simulating agents
from HARK.interpolation import(
LinearInterp, # Piecewise linear interpolation
CubicInterp, # Piecewise cubic interpolation
@@ -134,7 +134,7 @@ class PortfolioConsumerType(IndShockConsumerType):
time_inv_ = deepcopy(IndShockConsumerType.time_inv_)
time_inv_ = time_inv_ + ['AdjustPrb', 'DiscreteShareBool']
- def __init__(self, cycles=1, time_flow=True, verbose=False, quiet=False, **kwds):
+ def __init__(self, cycles=1, verbose=False, quiet=False, **kwds):
params = init_portfolio.copy()
params.update(kwds)
kwds = params
@@ -143,7 +143,6 @@ def __init__(self, cycles=1, time_flow=True, verbose=False, quiet=False, **kwds)
IndShockConsumerType.__init__(
self,
cycles=cycles,
- time_flow=time_flow,
verbose=verbose,
quiet=quiet,
**kwds
@@ -238,8 +237,6 @@ def updateRiskyDstn(self):
# agent has age-varying beliefs about the risky asset
if 'RiskyAvg' in self.time_vary:
RiskyDstn = []
- time_orig = self.time_flow
- self.timeFwd()
for t in range(self.T_cycle):
RiskyAvgSqrd = self.RiskyAvg[t] ** 2
RiskyVar = self.RiskyStd[t] ** 2
@@ -248,8 +245,6 @@ def updateRiskyDstn(self):
RiskyDstn.append(approxLognormal(self.RiskyCount, mu=mu, sigma=sigma))
self.RiskyDstn = RiskyDstn
self.addToTimeVary('RiskyDstn')
- if not time_orig:
- self.timeRev()
# Generate a discrete approximation to the risky return distribution if the
# agent does *not* have age-varying beliefs about the risky asset (base case)
@@ -317,8 +312,6 @@ def updateShareLimit(self):
None
'''
if 'RiskyDstn' in self.time_vary:
- time_orig = self.time_flow
- self.timeFwd()
self.ShareLimit = []
for t in range(self.T_cycle):
RiskyDstn = self.RiskyDstn[t]
@@ -326,8 +319,6 @@ def updateShareLimit(self):
SharePF = minimize_scalar(temp_f, bounds=(0.0, 1.0), method='bounded').x
self.ShareLimit.append(SharePF)
self.addToTimeVary('ShareLimit')
- if not time_orig:
- self.timeRev()
else:
RiskyDstn = self.RiskyDstn
@@ -362,7 +353,7 @@ def getRisky(self):
mu = np.log(RiskyAvg / (np.sqrt(1. + RiskyVar / RiskyAvgSqrd)))
sigma = np.sqrt(np.log(1. + RiskyVar / RiskyAvgSqrd))
- self.RiskyNow = drawLognormal(1, mu=mu, sigma=sigma, seed=self.RNG.randint(0, 2**31-1))
+ self.RiskyNow = Lognormal(mu, sigma).draw(1, seed=self.RNG.randint(0, 2**31-1))
def getAdjust(self):
@@ -379,7 +370,7 @@ def getAdjust(self):
-------
None
'''
- self.AdjustNow = drawBernoulli(self.AgentCount, p=self.AdjustPrb, seed=self.RNG.randint(0, 2**31-1))
+ self.AdjustNow = Bernoulli(self.AdjustPrb).draw(self.AgentCount, seed=self.RNG.randint(0, 2**31-1))
def getRfree(self):
diff --git a/HARK/ConsumptionSaving/ConsPrefShockModel.py b/HARK/ConsumptionSaving/ConsPrefShockModel.py
index b5b564727..a8e1b3925 100644
--- a/HARK/ConsumptionSaving/ConsPrefShockModel.py
+++ b/HARK/ConsumptionSaving/ConsPrefShockModel.py
@@ -50,7 +50,6 @@ class PrefShockConsumerType(IndShockConsumerType):
def __init__(self,
cycles=1,
- time_flow=True,
**kwds):
'''
Instantiate a new ConsumerType with given data, and construct objects
@@ -62,8 +61,6 @@ def __init__(self,
----------
cycles : int
Number of times the sequence of periods should be solved.
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
Returns
-------
@@ -74,7 +71,6 @@ def __init__(self,
IndShockConsumerType.__init__(self,
cycles=cycles,
- time_flow=time_flow,
**params)
self.solveOnePeriod = solveConsPrefShock # Choose correct solver
@@ -112,9 +108,6 @@ def updatePrefShockProcess(self):
-------
none
'''
- time_orig = self.time_flow
- self.timeFwd()
-
PrefShkDstn = [] # discrete distributions of preference shocks
for t in range(len(self.PrefShkStd)):
PrefShkStd = self.PrefShkStd[t]
@@ -124,8 +117,6 @@ def updatePrefShockProcess(self):
# Store the preference shocks in self (time-varying) and restore time flow
self.PrefShkDstn = PrefShkDstn
self.addToTimeVary('PrefShkDstn')
- if not time_orig:
- self.timeRev()
def getShocks(self):
'''
@@ -224,7 +215,7 @@ class KinkyPrefConsumerType(PrefShockConsumerType,KinkedRconsumerType):
utility each period, specified as iid lognormal and different interest rates
on borrowing vs saving.
'''
- def __init__(self,cycles=1,time_flow=True,**kwds):
+ def __init__(self,cycles=1,**kwds):
'''
Instantiate a new ConsumerType with given data, and construct objects
to be used during solution (income distribution, assets grid, etc).
@@ -235,8 +226,6 @@ def __init__(self,cycles=1,time_flow=True,**kwds):
----------
cycles : int
Number of times the sequence of periods should be solved.
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
Returns
-------
diff --git a/HARK/ConsumptionSaving/ConsRepAgentModel.py b/HARK/ConsumptionSaving/ConsRepAgentModel.py
index cf0c37b20..577a7c844 100644
--- a/HARK/ConsumptionSaving/ConsRepAgentModel.py
+++ b/HARK/ConsumptionSaving/ConsRepAgentModel.py
@@ -10,7 +10,7 @@
from builtins import range
import numpy as np
from HARK.interpolation import LinearInterp
-from HARK.simulation import drawUniform
+from HARK.distribution import Uniform
from HARK.ConsumptionSaving.ConsIndShockModel import IndShockConsumerType,\
ConsumerSolution,MargValueFunc, init_idiosyncratic_shocks
@@ -195,14 +195,12 @@ class RepAgentConsumerType(IndShockConsumerType):
'''
time_inv_ = IndShockConsumerType.time_inv_ + ['CapShare','DeprFac']
- def __init__(self,time_flow=True,**kwds):
+ def __init__(self,**kwds):
'''
Make a new instance of a representative agent.
Parameters
----------
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
Returns
-------
@@ -211,7 +209,7 @@ def __init__(self,time_flow=True,**kwds):
params = init_rep_agent.copy()
params.update(kwds)
- IndShockConsumerType.__init__(self,cycles=0,time_flow=time_flow,**params)
+ IndShockConsumerType.__init__(self,cycles=0,**params)
self.AgentCount = 1 # Hardcoded, because this is rep agent
self.solveOnePeriod = solveConsRepAgent
self.delFromTimeInv('Rfree','BoroCnstArt','vFuncBool','CubicBool')
@@ -251,23 +249,21 @@ class RepAgentMarkovConsumerType(RepAgentConsumerType):
'''
time_inv_ = RepAgentConsumerType.time_inv_ + ['MrkvArray']
- def __init__(self,time_flow=True,**kwds):
+ def __init__(self,**kwds):
'''
Make a new instance of a representative agent with Markov state.
Parameters
----------
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
-
+
Returns
-------
None
'''
params = init_markov_rep_agent.copy()
params.update(kwds)
-
- RepAgentConsumerType.__init__(self,time_flow=time_flow,**params)
+
+ RepAgentConsumerType.__init__(self,**params)
self.solveOnePeriod = solveConsRepAgentMarkov
def preSolve(self):
@@ -308,7 +304,7 @@ def getShocks(self):
None
'''
cutoffs = np.cumsum(self.MrkvArray[self.MrkvNow,:])
- MrkvDraw = drawUniform(N=1,seed=self.RNG.randint(0,2**31-1))
+ MrkvDraw = Uniform().draw(N=1,seed=self.RNG.randint(0,2**31-1))
self.MrkvNow = np.searchsorted(cutoffs,MrkvDraw)
t = self.t_cycle[0]
@@ -339,8 +335,7 @@ def getControls(self):
t = self.t_cycle[0]
i = self.MrkvNow[0]
self.cNrmNow = self.solution[t].cFunc[i](self.mNrmNow)
-
-
+
# Define the default dictionary for a representative agent type
init_rep_agent = init_idiosyncratic_shocks.copy()
init_rep_agent["DeprFac"] = 0.05
diff --git a/HARK/ConsumptionSaving/TractableBufferStockModel.py b/HARK/ConsumptionSaving/TractableBufferStockModel.py
index f47425fe2..5ff678218 100644
--- a/HARK/ConsumptionSaving/TractableBufferStockModel.py
+++ b/HARK/ConsumptionSaving/TractableBufferStockModel.py
@@ -30,7 +30,7 @@
from HARK.utilities import warnings # Because of "patch" to warnings modules
from HARK.utilities import CRRAutility, CRRAutilityP, CRRAutilityPP, CRRAutilityPPP, CRRAutilityPPPP, CRRAutilityP_inv, CRRAutility_invP, CRRAutility_inv
from HARK.interpolation import CubicInterp
-from HARK.simulation import drawLognormal, drawBernoulli
+from HARK.distribution import Lognormal, Bernoulli
from copy import copy
from scipy.optimize import newton, brentq
@@ -226,7 +226,7 @@ def addToStableArmPoints(solution_next,DiscFac,Rfree,CRRA,PermGroFacCmp,UnempPrb
class TractableConsumerType(AgentType):
- def __init__(self,cycles=0,time_flow=False,**kwds):
+ def __init__(self,cycles=0,**kwds):
'''
Instantiate a new TractableConsumerType with given data.
@@ -234,15 +234,15 @@ def __init__(self,cycles=0,time_flow=False,**kwds):
----------
cycles : int
Number of times the sequence of periods should be solved.
- time_flow : boolean
- Whether time is currently "flowing" forward for this instance.
Returns:
-----------
New instance of TractableConsumerType.
'''
# Initialize a basic AgentType
- AgentType.__init__(self,cycles=cycles,time_flow=time_flow,pseudo_terminal=True,**kwds)
+ AgentType.__init__(self,
+ cycles=cycles,
+ pseudo_terminal=True,**kwds)
# Add consumer-type specific objects, copying to create independent versions
self.time_vary = []
@@ -378,7 +378,8 @@ def simBirth(self,which_agents):
'''
# Get and store states for newly born agents
N = np.sum(which_agents) # Number of new consumers to make
- self.aLvlNow[which_agents] = drawLognormal(N,mu=self.aLvlInitMean,sigma=self.aLvlInitStd,seed=self.RNG.randint(0,2**31-1))
+ self.aLvlNow[which_agents] = Lognormal(self.aLvlInitMean,
+ sigma=self.aLvlInitStd).draw(N,seed=self.RNG.randint(0,2**31-1))
self.eStateNow[which_agents] = 1.0 # Agents are born employed
self.t_age[which_agents] = 0 # How many periods since each agent was born
self.t_cycle[which_agents] = 0 # Which period of the cycle each agent is currently in
@@ -416,7 +417,8 @@ def getShocks(self):
'''
employed = self.eStateNow == 1.0
N = int(np.sum(employed))
- newly_unemployed = drawBernoulli(N,p=self.UnempPrb,seed=self.RNG.randint(0,2**31-1))
+ newly_unemployed = Bernoulli(self.UnempPrb).draw(N,
+ seed=self.RNG.randint(0,2**31-1))
self.eStateNow[employed] = 1.0 - newly_unemployed
def getStates(self):
diff --git a/HARK/ConsumptionSaving/tests/test_ConsMarkovModel.py b/HARK/ConsumptionSaving/tests/test_ConsMarkovModel.py
index fb951b014..a91629c8c 100644
--- a/HARK/ConsumptionSaving/tests/test_ConsMarkovModel.py
+++ b/HARK/ConsumptionSaving/tests/test_ConsMarkovModel.py
@@ -1,6 +1,7 @@
import numpy as np
from HARK.ConsumptionSaving.ConsIndShockModel import init_idiosyncratic_shocks
from HARK.ConsumptionSaving.ConsMarkovModel import MarkovConsumerType
+from HARK.distribution import DiscreteDistribution
from copy import copy
import unittest
@@ -17,7 +18,7 @@ def setUp(self):
p_unemploy_good = p_reemploy * urate_good / (1 - urate_good)
p_unemploy_bad = p_reemploy * urate_bad / (1 - urate_bad)
boom_prob = 1.0 / recession_length
- self.MrkvArray = np.array(
+ MrkvArray = np.array(
[
[
(1 - p_unemploy_good) * (1 - bust_prob),
@@ -47,15 +48,32 @@ def setUp(self):
)
init_serial_unemployment = copy(init_idiosyncratic_shocks)
- init_serial_unemployment["MrkvArray"] = [self.MrkvArray]
- self.model = MarkovConsumerType(**init_serial_unemployment)
-
+ init_serial_unemployment["MrkvArray"] = [MrkvArray]
+ init_serial_unemployment["UnempPrb"] = 0 # to make income distribution when employed
+ init_serial_unemployment["global_markov"] = False
+ self.model = MarkovConsumerType(**init_serial_unemployment)
+ self.model.cycles = 0
+ self.model.vFuncBool = False # for easy toggling here
+
+ # Replace the default (lognormal) income distribution with a custom one
+ employed_income_dist = DiscreteDistribution(np.ones(1), [np.ones(1), np.ones(1)]) # Definitely get income
+ unemployed_income_dist = DiscreteDistribution(np.ones(1), [np.ones(1), np.zeros(1)]) # Definitely don't
+ self.model.IncomeDstn = [
+ [
+ employed_income_dist,
+ unemployed_income_dist,
+ employed_income_dist,
+ unemployed_income_dist,
+ ]
+ ]
+
def test_checkMarkovInputs(self):
# check Rfree
self.assertRaises(ValueError, self.model.checkMarkovInputs)
# fix Rfree
self.model.Rfree = np.array(4 * [self.model.Rfree])
# check MrkvArray, first mess up the setup
+ self.MrkvArray = self.model.MrkvArray
self.model.MrkvArray = np.random.rand(3, 3)
self.assertRaises(ValueError, self.model.checkMarkovInputs)
# then fix it back
@@ -68,3 +86,7 @@ def test_checkMarkovInputs(self):
self.assertRaises(ValueError, self.model.checkMarkovInputs)
# fix PermGroFac
self.model.PermGroFac = [np.array(4 * self.model.PermGroFac)]
+
+ def test_solve(self):
+ self.test_checkMarkovInputs()
+ self.model.solve()
diff --git a/HARK/ConsumptionSaving/tests/test_IndShockConsumerType.py b/HARK/ConsumptionSaving/tests/test_IndShockConsumerType.py
index 7a691cde3..75e6c777f 100644
--- a/HARK/ConsumptionSaving/tests/test_IndShockConsumerType.py
+++ b/HARK/ConsumptionSaving/tests/test_IndShockConsumerType.py
@@ -35,17 +35,40 @@ def test_ConsIndShockSolverBasic(self):
LifecycleExample.cycles = 1
LifecycleExample.solve()
- solver = ConsIndShockSolverBasic(LifecycleExample.solution[1],
- LifecycleExample.IncomeDstn[0],
- LifecycleExample.LivPrb[0],
- LifecycleExample.DiscFac,
- LifecycleExample.CRRA,
- LifecycleExample.Rfree,
- LifecycleExample.PermGroFac[0],
- LifecycleExample.BoroCnstArt,
- LifecycleExample.aXtraGrid,
- LifecycleExample.vFuncBool,
- LifecycleExample.CubicBool)
+ # test the solution_terminal
+ self.assertAlmostEqual(
+ LifecycleExample.solution[10].cFunc(2).tolist(),
+ 2)
+
+ self.assertAlmostEqual(LifecycleExample.solution[9].cFunc(1),
+ 0.97769632)
+ self.assertAlmostEqual(LifecycleExample.solution[8].cFunc(1),
+ 0.96624445)
+ self.assertAlmostEqual(LifecycleExample.solution[7].cFunc(1),
+ 0.95691449)
+
+ self.assertAlmostEqual(
+ LifecycleExample.solution[0].cFunc(1).tolist(),
+ 0.87362789)
+ self.assertAlmostEqual(
+ LifecycleExample.solution[1].cFunc(1).tolist(),
+ 0.9081621)
+ self.assertAlmostEqual(
+ LifecycleExample.solution[2].cFunc(1).tolist(),
+ 0.9563899)
+
+ solver = ConsIndShockSolverBasic(
+ LifecycleExample.solution[1],
+ LifecycleExample.IncomeDstn[0],
+ LifecycleExample.LivPrb[0],
+ LifecycleExample.DiscFac,
+ LifecycleExample.CRRA,
+ LifecycleExample.Rfree,
+ LifecycleExample.PermGroFac[0],
+ LifecycleExample.BoroCnstArt,
+ LifecycleExample.aXtraGrid,
+ LifecycleExample.vFuncBool,
+ LifecycleExample.CubicBool)
solver.prepareToSolve()
@@ -301,7 +324,7 @@ def test_lifecyle(self):
self.assertAlmostEqual(LifecycleExample.solution[5].cFunc(3).tolist(),
2.129983771775666)
-CyclicalDict = { # Click the arrow to expand this parameter dictionary
+CyclicalDict = {
# Parameters shared with the perfect foresight model
"CRRA": 2.0, # Coefficient of relative risk aversion
"Rfree": 1.03, # Interest factor on assets
diff --git a/HARK/ConsumptionSaving/tests/test_modelcomparisons.py b/HARK/ConsumptionSaving/tests/test_modelcomparisons.py
index ff9492c1b..736bfe96c 100644
--- a/HARK/ConsumptionSaving/tests/test_modelcomparisons.py
+++ b/HARK/ConsumptionSaving/tests/test_modelcomparisons.py
@@ -49,7 +49,6 @@ def setUp(self):
InfiniteType.updateIncomeProcess()
InfiniteType.solve()
- InfiniteType.timeFwd()
InfiniteType.unpackcFunc()
# Make and solve a perfect foresight consumer type with the same parameters
@@ -58,7 +57,6 @@ def setUp(self):
PerfectForesightType.solve()
PerfectForesightType.unpackcFunc()
- PerfectForesightType.timeFwd()
self.InfiniteType = InfiniteType
self.PerfectForesightType = PerfectForesightType
diff --git a/HARK/core.py b/HARK/core.py
index b4b8c2a03..6dcd7acab 100644
--- a/HARK/core.py
+++ b/HARK/core.py
@@ -173,7 +173,7 @@ class AgentType(HARKobject):
that varies over time in the model. Each element of time_inv is the name of
a field in AgentSubType that is constant over time in the model.
'''
- def __init__(self, solution_terminal=None, cycles=1, time_flow=True, pseudo_terminal=True,
+ def __init__(self, solution_terminal=None, cycles=1, pseudo_terminal=True,
tolerance=0.000001, seed=0, **kwds):
'''
Initialize an instance of AgentType by setting attributes.
@@ -190,10 +190,6 @@ def __init__(self, solution_terminal=None, cycles=1, time_flow=True, pseudo_term
model, with a certain sequence of one period problems experienced
once before terminating. cycles=0 corresponds to an infinite horizon
model, with a sequence of one period problems repeating indefinitely.
- time_flow : boolean
- Whether time is currently "flowing" forward(True) or backward(False) for this
- instance. Used to flip between solving (using backward iteration)
- and simulating (etc).
pseudo_terminal : boolean
Indicates whether solution_terminal isn't actually part of the
solution to the problem (as a known solution to the terminal period
@@ -216,7 +212,6 @@ def __init__(self, solution_terminal=None, cycles=1, time_flow=True, pseudo_term
solution_terminal = NullFunc()
self.solution_terminal = solution_terminal # NOQA
self.cycles = cycles # NOQA
- self.time_flow = time_flow # NOQA
self.pseudo_terminal = pseudo_terminal # NOQA
self.solveOnePeriod = NullFunc() # NOQA
self.tolerance = tolerance # NOQA
@@ -227,70 +222,6 @@ def __init__(self, solution_terminal=None, cycles=1, time_flow=True, pseudo_term
self.assignParameters(**kwds) # NOQA
self.resetRNG() # NOQA
- def timeReport(self):
- '''
- Report to the user the direction that time is currently "flowing" for
- this instance. Only exists as a reminder of how time_flow works.
-
- Parameters
- ----------
- none
-
- Returns
- -------
- none
- '''
- if self.time_flow:
- print('Time varying objects are listed in ordinary chronological order.')
- else:
- print('Time varying objects are listed in reverse chronological order.')
-
- def timeFlip(self):
- '''
- Reverse the flow of time for this instance.
-
- Parameters
- ----------
- none
-
- Returns
- -------
- none
- '''
- for name in self.time_vary:
- self.__dict__[name].reverse()
- self.time_flow = not self.time_flow
-
- def timeFwd(self):
- '''
- Make time flow forward for this instance.
-
- Parameters
- ----------
- none
-
- Returns
- -------
- none
- '''
- if not self.time_flow:
- self.timeFlip()
-
- def timeRev(self):
- '''
- Make time flow backward for this instance.
-
- Parameters
- ----------
- none
-
- Returns
- -------
- none
- '''
- if self.time_flow:
- self.timeFlip()
-
def addToTimeVary(self, *params):
'''
Adds any number of parameters to time_vary for this instance.
@@ -381,9 +312,6 @@ def solve(self, verbose=False):
with np.errstate(divide='ignore', over='ignore', under='ignore', invalid='ignore'):
self.preSolve() # Do pre-solution stuff
self.solution = solveAgent(self, verbose) # Solve the model by backward induction
- if self.time_flow: # Put the solution in chronological order if this instance's time flow runs that way
- self.solution.reverse()
- self.addToTimeVary('solution') # Add solution to the list of time-varying attributes
self.postSolve() # Do post-solution stuff
def resetRNG(self):
@@ -529,9 +457,7 @@ def makeShockHistory(self):
-------
None
'''
- # Make sure time is flowing forward and re-initialize the simulation
- orig_time = self.time_flow
- self.timeFwd()
+ # Re-initialize the simulation
self.initializeSim()
# Make blank history arrays for each shock variable (and mortality)
@@ -551,10 +477,8 @@ def makeShockHistory(self):
self.t_cycle = self.t_cycle + 1 # Age all consumers within their cycle
self.t_cycle[self.t_cycle == self.T_cycle] = 0 # Resetting to zero for those who have reached the end
- # Restore the flow of time and flag that shocks can be read rather than simulated
+ # Flag that shocks can be read rather than simulated
self.read_shocks = True
- if not orig_time:
- self.timeRev()
def getMortality(self):
'''
@@ -729,8 +653,6 @@ def simulate(self, sim_periods=None):
# tions with well-defined answers such as 1.0/0.0 that is np.inf, -1.0/0.0 that is
# -np.inf, np.inf/np.inf is np.nan and so on.
with np.errstate(divide='ignore', over='ignore', under='ignore', invalid='ignore'):
- orig_time = self.time_flow
- self.timeFwd()
if sim_periods is None:
sim_periods = self.T_sim
@@ -740,9 +662,6 @@ def simulate(self, sim_periods=None):
getattr(self, var_name + '_hist')[self.t_sim,:] = getattr(self,var_name)
self.t_sim += 1
- if not orig_time:
- self.timeRev()
-
def clearHistory(self):
'''
Clears the histories of the attributes named in self.track_vars.
@@ -761,14 +680,19 @@ def clearHistory(self):
def solveAgent(agent, verbose):
'''
- Solve the dynamic model for one agent type. This function iterates on "cycles"
- of an agent's model either a given number of times or until solution convergence
- if an infinite horizon model is used (with agent.cycles = 0).
+ Solve the dynamic model for one agent type
+ using backwards induction.
+ This function iterates on "cycles"
+ of an agent's model either a given number of times
+ or until solution convergence
+ if an infinite horizon model is used
+ (with agent.cycles = 0).
Parameters
----------
agent : AgentType
- The microeconomic AgentType whose dynamic problem is to be solved.
+ The microeconomic AgentType whose dynamic problem
+ is to be solved.
verbose : boolean
If True, solution progress is printed to screen (when cycles != 1).
@@ -776,19 +700,15 @@ def solveAgent(agent, verbose):
-------
solution : [Solution]
A list of solutions to the one period problems that the agent will
- encounter in his "lifetime". Returns in reverse chronological order.
+ encounter in his "lifetime".
'''
- # Record the flow of time when the Agent began the process, and make sure time is flowing backwards
- original_time_flow = agent.time_flow
- agent.timeRev()
-
# Check to see whether this is an (in)finite horizon problem
cycles_left = agent.cycles # NOQA
infinite_horizon = cycles_left == 0 # NOQA
# Initialize the solution, which includes the terminal solution if it's not a pseudo-terminal period
solution = []
if not agent.pseudo_terminal:
- solution.append(deepcopy(agent.solution_terminal))
+ solution.insert(0, deepcopy(agent.solution_terminal))
# Initialize the process, then loop over cycles
@@ -802,10 +722,11 @@ def solveAgent(agent, verbose):
# Solve a cycle of the model, recording it if horizon is finite
solution_cycle = solveOneCycle(agent, solution_last)
if not infinite_horizon:
- solution += solution_cycle
+ solution = solution_cycle + solution
- # Check for termination: identical solutions across cycle iterations or run out of cycles
- solution_now = solution_cycle[-1]
+ # Check for termination: identical solutions across
+ # cycle iterations or run out of cycles
+ solution_now = solution_cycle[0]
if infinite_horizon:
if completed_cycles > 0:
solution_distance = solution_now.distance(solution_last)
@@ -838,9 +759,6 @@ def solveAgent(agent, verbose):
if infinite_horizon:
solution = solution_cycle # PseudoTerminal=False impossible for infinite horizon
- # Restore the direction of time to its original orientation, then return the solution
- if original_time_flow:
- agent.timeFwd()
return solution
@@ -864,7 +782,7 @@ def solveOneCycle(agent, solution_last):
-------
solution_cycle : [Solution]
A list of one period solutions for one "cycle" of the AgentType's
- microeconomic model. Returns in reverse chronological order.
+ microeconomic model.
'''
# Calculate number of periods per cycle, defaults to 1 if all variables are time invariant
if len(agent.time_vary) > 0:
@@ -874,16 +792,12 @@ def solveOneCycle(agent, solution_last):
else:
T = 1
- # Construct a dictionary to be passed to the solver
- # time_inv_string = ''
- # for name in agent.time_inv:
- # time_inv_string += ' \'' + name + '\' : agent.' + name + ','
- # time_vary_string = ''
- # for name in agent.time_vary:
- # time_vary_string += ' \'' + name + '\' : None,'
- # solve_dict = eval('{' + time_inv_string + time_vary_string + '}')
- solve_dict = {parameter: agent.__dict__[parameter] for parameter in agent.time_inv}
- solve_dict.update({parameter: None for parameter in agent.time_vary})
+ solve_dict = {parameter: agent.__dict__[parameter]
+ for parameter
+ in agent.time_inv}
+ solve_dict.update({parameter: None
+ for parameter
+ in agent.time_vary})
# Initialize the solution for this cycle, then iterate on periods
solution_cycle = []
@@ -901,15 +815,17 @@ def solveOneCycle(agent, solution_last):
for name in agent.time_vary:
if name in these_args:
# solve_dict[name] = eval('agent.' + name + '[t]')
- solve_dict[name] = agent.__dict__[name][t]
+ solve_dict[name] = agent.__dict__[name][T - 1 - t]
solve_dict['solution_next'] = solution_next
# Make a temporary dictionary for this period
- temp_dict = {name: solve_dict[name] for name in these_args}
+ temp_dict = {name: solve_dict[name]
+ for name
+ in these_args}
# Solve one period, add it to the solution, and move to the next period
solution_t = solveOnePeriod(**temp_dict)
- solution_cycle.append(solution_t)
+ solution_cycle.insert(0, solution_t)
solution_next = solution_t
# Return the list of per-period solutions
diff --git a/HARK/distribution.py b/HARK/distribution.py
index b818d60fd..4f0a431ad 100644
--- a/HARK/distribution.py
+++ b/HARK/distribution.py
@@ -5,6 +5,328 @@
import scipy.stats as stats
import warnings
+### CONTINUOUS DISTRIBUTIONS
+
+class Lognormal():
+ """
+ A Lognormal distribution
+ """
+ mu = None
+ sigma = None
+
+ def __init__(self, mu = 0.0, sigma = 1.0):
+ '''
+ Initialize the distribution.
+
+ Parameters
+ ----------
+ mu : float or [float]
+ One or more means. Number of elements T in mu determines number
+ of rows of output.
+ sigma : float or [float]
+ One or more standard deviations. Number of elements T in sigma
+ determines number of rows of output.
+ '''
+ self.mu = mu
+ self.sigma = sigma
+
+ def draw(self, N, seed=0):
+ '''
+ Generate arrays of lognormal draws. The sigma input can be a number
+ or list-like. If a number, output is a length N array of draws from the
+ lognormal distribution with standard deviation sigma. If a list, output is
+ a length T list whose t-th entry is a length N array of draws from the
+ lognormal with standard deviation sigma[t].
+
+ Parameters
+ ----------
+ N : int
+ Number of draws in each row.
+ seed : int
+ Seed for random number generator.
+
+ Returns:
+ ------------
+ draws : np.array or [np.array]
+ T-length list of arrays of mean one lognormal draws each of size N, or
+ a single array of size N (if sigma is a scalar).
+ '''
+ # Set up the RNG
+ RNG = np.random.RandomState(seed)
+
+ if isinstance(self.sigma,float): # Return a single array of length N
+ if self.sigma == 0:
+ draws = np.exp(self.mu)*np.ones(N)
+ else:
+ draws = RNG.lognormal(mean=self.mu,
+ sigma=self.sigma,
+ size=N)
+ else: # Set up empty list to populate, then loop and populate list with draws
+ draws=[]
+ for j in range(len(self.sigma)):
+ if self.sigma[j] == 0:
+ draws.append(np.exp(self.mu[j])*np.ones(N))
+ else:
+ draws.append(RNG.lognormal(mean=self.mu[j],
+ sigma=self.sigma[j],
+ size=N))
+ return draws
+
+class Normal():
+ """
+ A Normal distribution.
+ """
+ mu = None
+ sigma = None
+
+ def __init__(self, mu = 0.0, sigma = 1.0):
+ '''
+ Initialize the distribution.
+
+ Parameters
+ ----------
+ mu : float or [float]
+ One or more means. Number of elements T in mu determines number
+ of rows of output.
+ sigma : float or [float]
+ One or more standard deviations. Number of elements T in sigma
+ determines number of rows of output.
+ '''
+ self.mu = 0.0
+ self.sigma = 1.0
+
+ def draw(self, N, seed=0):
+ '''
+ Generate arrays of normal draws. The mu and sigma inputs can be numbers or
+ list-likes. If a number, output is a length N array of draws from the normal
+ distribution with mean mu and standard deviation sigma. If a list, output is
+ a length T list whose t-th entry is a length N array with draws from the
+ normal distribution with mean mu[t] and standard deviation sigma[t].
+
+ Parameters
+ ----------
+ N : int
+ Number of draws in each row.
+ seed : int
+ Seed for random number generator.
+
+ Returns
+ -------
+ draws : np.array or [np.array]
+ T-length list of arrays of normal draws each of size N, or a single array
+ of size N (if sigma is a scalar).
+ '''
+ # Set up the RNG
+ RNG = np.random.RandomState(seed)
+
+ if isinstance(self.sigma,float): # Return a single array of length N
+ draws = self.sigma*RNG.randn(N) + self.mu
+ else: # Set up empty list to populate, then loop and populate list with draws
+ draws=[]
+ for t in range(len(sigma)):
+ draws.append(self.sigma[t]*RNG.randn(N) + self.mu[t])
+ return draws
+
+class Weibull():
+ '''
+ A Weibull distribution
+ '''
+
+ scale = None
+ shape = None
+
+ def __init__(self, scale=1.0, shape=1.0):
+ '''
+ Initialize the distribution.
+
+ Parameters
+ ----------
+ scale : float or [float]
+ One or more scales. Number of elements T in scale determines number of
+ rows of output.
+ shape : float or [float]
+ One or more shape parameters. Number of elements T in scale
+ determines number of rows of output.
+ '''
+ self.scale = scale
+ self.shape = shape
+
+ def draw(self, N, seed=0):
+ '''
+ Generate arrays of Weibull draws. The scale and shape inputs can be
+ numbers or list-likes. If a number, output is a length N array of draws from
+ the Weibull distribution with the given scale and shape. If a list, output
+ is a length T list whose t-th entry is a length N array with draws from the
+ Weibull distribution with scale scale[t] and shape shape[t].
+
+ Note: When shape=1, the Weibull distribution is simply the exponential dist.
+
+ Mean: scale*Gamma(1 + 1/shape)
+
+ Parameters
+ ----------
+ N : int
+ Number of draws in each row.
+ seed : int
+ Seed for random number generator.
+
+ Returns:
+ ------------
+ draws : np.array or [np.array]
+ T-length list of arrays of Weibull draws each of size N, or a single
+ array of size N (if sigma is a scalar).
+ '''
+ # Set up the RNG
+ RNG = np.random.RandomState(seed)
+
+ if self.scale == 1:
+ scale = float(self.scale)
+ if isinstance(self.scale,float): # Return a single array of length N
+ draws = self.scale*(-np.log(1.0-RNG.rand(N)))**(1.0/self.shape)
+ else: # Set up empty list to populate, then loop and populate list with draws
+ draws=[]
+ for t in range(len(self.scale)):
+ draws.append(self.scale[t]*(-np.log(1.0-RNG.rand(N)))**(1.0/self.shape[t]))
+ return draws
+
+class Uniform():
+ """
+ A Uniform distribution.
+ """
+
+ bot = None
+ top = None
+
+ def __init__(self, bot = 0.0, top = 1.0):
+ '''
+ Initialize the distribution.
+
+ Parameters
+ ----------
+ bot : float or [float]
+ One or more bottom values. Number of elements T in mu determines number
+ of rows of output.
+ top : float or [float]
+ One or more top values. Number of elements T in top determines number of
+ rows of output.
+ '''
+ self.bot = bot
+ self.top = top
+
+ def draw(self, N, seed=0):
+ '''
+ Generate arrays of uniform draws. The bot and top inputs can be numbers or
+ list-likes. If a number, output is a length N array of draws from the
+ uniform distribution on [bot,top]. If a list, output is a length T list
+ whose t-th entry is a length N array with draws from the uniform distribution
+ on [bot[t],top[t]].
+
+ Parameters
+ ----------
+ N : int
+ Number of draws in each row.
+ seed : int
+ Seed for random number generator.
+
+ Returns
+ -------
+ draws : np.array or [np.array]
+ T-length list of arrays of uniform draws each of size N, or a single
+ array of size N (if sigma is a scalar).
+ '''
+ # Set up the RNG
+ RNG = np.random.RandomState(seed)
+
+ if isinstance(self.bot,float) or isinstance(self.bot,int): # Return a single array of size N
+ draws = self.bot + (self.top - self.bot)*RNG.rand(N)
+ else: # Set up empty list to populate, then loop and populate list with draws
+ draws=[]
+ for t in range(len(bot)):
+ draws.append(self.bot[t] + (self.top[t] - self.bot[t])*RNG.rand(N))
+ return draws
+
+
+def drawMeanOneLognormal(N, sigma=1.0, seed=0):
+ '''
+ Generate arrays of mean one lognormal draws. The sigma input can be a number
+ or list-like. If a number, output is a length N array of draws from the
+ lognormal distribution with standard deviation sigma. If a list, output is
+ a length T list whose t-th entry is a length N array of draws from the
+ lognormal with standard deviation sigma[t].
+
+ Parameters
+ ----------
+ N : int
+ Number of draws in each row.
+ sigma : float or [float]
+ One or more standard deviations. Number of elements T in sigma
+ determines number of rows of output.
+ seed : int
+ Seed for random number generator.
+
+ Returns:
+ ------------
+ draws : np.array or [np.array]
+ T-length list of arrays of mean one lognormal draws each of size N, or
+ a single array of size N (if sigma is a scalar).
+ '''
+ mu = -0.5*sigma**2
+
+ return Lognormal(mu,sigma).draw(N,seed=seed)
+
+
+### DISCRETE DISTRIBUTIONS
+
+class Bernoulli():
+ """
+ A Bernoulli distribution.
+ """
+
+ p = None
+
+ def __init__(self, p = 0.5):
+ '''
+ Initialize the distribution.
+
+ Parameters
+ ----------
+ p : float or [float]
+ Probability or probabilities of the event occurring (True).
+ '''
+ self.p = p
+
+ def draw(self, N, seed = 0):
+ '''
+ Generates arrays of booleans drawn from a simple Bernoulli distribution.
+ The input p can be a float or a list-like of floats; its length T determines
+ the number of entries in the output. The t-th entry of the output is an
+ array of N booleans which are True with probability p[t] and False otherwise.
+
+ Arguments
+ ---------
+ N : int
+ Number of draws in each row.
+ seed : int
+ Seed for random number generator.
+
+ Returns
+ -------
+ draws : np.array or [np.array]
+ T-length list of arrays of Bernoulli draws each of size N, or a single
+ array of size N (if sigma is a scalar).
+ '''
+ # Set up the RNG
+ RNG = np.random.RandomState(seed)
+
+ if isinstance(self.p,float):# Return a single array of size N
+ draws = RNG.uniform(size=N) < self.p
+ else: # Set up empty list to populate, then loop and populate list with draws:
+ draws=[]
+ for t in range(len(self.p)):
+ draws.append(RNG.uniform(size=N) < self.p[t])
+ return draws
+
+
class DiscreteDistribution():
"""
diff --git a/HARK/simulation.py b/HARK/simulation.py
index 74371ff38..4f41707d1 100644
--- a/HARK/simulation.py
+++ b/HARK/simulation.py
@@ -1,243 +1,8 @@
'''
-Functions for generating simulated data and shocks.
+Currently empty. Will be used for future simulation handling code.
'''
from __future__ import division
import warnings # A library for runtime warnings
import numpy as np # Numerical Python
-def drawMeanOneLognormal(N, sigma=1.0, seed=0):
- '''
- Generate arrays of mean one lognormal draws. The sigma input can be a number
- or list-like. If a number, output is a length N array of draws from the
- lognormal distribution with standard deviation sigma. If a list, output is
- a length T list whose t-th entry is a length N array of draws from the
- lognormal with standard deviation sigma[t].
-
- Parameters
- ----------
- N : int
- Number of draws in each row.
- sigma : float or [float]
- One or more standard deviations. Number of elements T in sigma
- determines number of rows of output.
- seed : int
- Seed for random number generator.
-
- Returns:
- ------------
- draws : np.array or [np.array]
- T-length list of arrays of mean one lognormal draws each of size N, or
- a single array of size N (if sigma is a scalar).
- '''
- mu = -0.5*sigma**2
-
- return drawLognormal(N,mu=mu,sigma=sigma,seed=seed)
-
-def drawLognormal(N,mu=0.0,sigma=1.0,seed=0):
- '''
- Generate arrays of lognormal draws. The sigma input can be a number
- or list-like. If a number, output is a length N array of draws from the
- lognormal distribution with standard deviation sigma. If a list, output is
- a length T list whose t-th entry is a length N array of draws from the
- lognormal with standard deviation sigma[t].
-
- Parameters
- ----------
- N : int
- Number of draws in each row.
- mu : float or [float]
- One or more means. Number of elements T in mu determines number
- of rows of output.
- sigma : float or [float]
- One or more standard deviations. Number of elements T in sigma
- determines number of rows of output.
- seed : int
- Seed for random number generator.
-
- Returns:
- ------------
- draws : np.array or [np.array]
- T-length list of arrays of mean one lognormal draws each of size N, or
- a single array of size N (if sigma is a scalar).
- '''
- # Set up the RNG
- RNG = np.random.RandomState(seed)
-
- if isinstance(sigma,float): # Return a single array of length N
- if sigma == 0:
- draws = np.exp(mu)*np.ones(N)
- else:
- draws = RNG.lognormal(mean=mu, sigma=sigma, size=N)
- else: # Set up empty list to populate, then loop and populate list with draws
- draws=[]
- for j in range(len(sigma)):
- if sigma[j] == 0:
- draws.append(np.exp(mu[j])*np.ones(N))
- else:
- draws.append(RNG.lognormal(mean=mu[j], sigma=sigma[j], size=N))
- return draws
-
-
-def drawNormal(N, mu=0.0, sigma=1.0, seed=0):
- '''
- Generate arrays of normal draws. The mu and sigma inputs can be numbers or
- list-likes. If a number, output is a length N array of draws from the normal
- distribution with mean mu and standard deviation sigma. If a list, output is
- a length T list whose t-th entry is a length N array with draws from the
- normal distribution with mean mu[t] and standard deviation sigma[t].
-
- Parameters
- ----------
- N : int
- Number of draws in each row.
- mu : float or [float]
- One or more means. Number of elements T in mu determines number of rows
- of output.
- sigma : float or [float]
- One or more standard deviations. Number of elements T in sigma
- determines number of rows of output.
- seed : int
- Seed for random number generator.
-
- Returns
- -------
- draws : np.array or [np.array]
- T-length list of arrays of normal draws each of size N, or a single array
- of size N (if sigma is a scalar).
- '''
- # Set up the RNG
- RNG = np.random.RandomState(seed)
-
- if isinstance(sigma,float): # Return a single array of length N
- draws = sigma*RNG.randn(N) + mu
- else: # Set up empty list to populate, then loop and populate list with draws
- draws=[]
- for t in range(len(sigma)):
- draws.append(sigma[t]*RNG.randn(N) + mu[t])
- return draws
-
-def drawWeibull(N, scale=1.0, shape=1.0, seed=0):
- '''
- Generate arrays of Weibull draws. The scale and shape inputs can be
- numbers or list-likes. If a number, output is a length N array of draws from
- the Weibull distribution with the given scale and shape. If a list, output
- is a length T list whose t-th entry is a length N array with draws from the
- Weibull distribution with scale scale[t] and shape shape[t].
-
- Note: When shape=1, the Weibull distribution is simply the exponential dist.
-
- Mean: scale*Gamma(1 + 1/shape)
-
- Parameters
- ----------
- N : int
- Number of draws in each row.
- scale : float or [float]
- One or more scales. Number of elements T in scale determines number of
- rows of output.
- shape : float or [float]
- One or more shape parameters. Number of elements T in scale
- determines number of rows of output.
- seed : int
- Seed for random number generator.
-
- Returns:
- ------------
- draws : np.array or [np.array]
- T-length list of arrays of Weibull draws each of size N, or a single
- array of size N (if sigma is a scalar).
- '''
- # Set up the RNG
- RNG = np.random.RandomState(seed)
-
- if scale == 1:
- scale = float(scale)
- if isinstance(scale,float): # Return a single array of length N
- draws = scale*(-np.log(1.0-RNG.rand(N)))**(1.0/shape)
- else: # Set up empty list to populate, then loop and populate list with draws
- draws=[]
- for t in range(len(scale)):
- draws.append(scale[t]*(-np.log(1.0-RNG.rand(N)))**(1.0/shape[t]))
- return draws
-
-def drawUniform(N, bot=0.0, top=1.0, seed=0):
- '''
- Generate arrays of uniform draws. The bot and top inputs can be numbers or
- list-likes. If a number, output is a length N array of draws from the
- uniform distribution on [bot,top]. If a list, output is a length T list
- whose t-th entry is a length N array with draws from the uniform distribution
- on [bot[t],top[t]].
-
- Parameters
- ----------
- N : int
- Number of draws in each row.
- bot : float or [float]
- One or more bottom values. Number of elements T in mu determines number
- of rows of output.
- top : float or [float]
- One or more top values. Number of elements T in top determines number of
- rows of output.
- seed : int
- Seed for random number generator.
-
- Returns
- -------
- draws : np.array or [np.array]
- T-length list of arrays of uniform draws each of size N, or a single
- array of size N (if sigma is a scalar).
- '''
- # Set up the RNG
- RNG = np.random.RandomState(seed)
-
- if isinstance(bot,float) or isinstance(bot,int): # Return a single array of size N
- draws = bot + (top - bot)*RNG.rand(N)
- else: # Set up empty list to populate, then loop and populate list with draws
- draws=[]
- for t in range(len(bot)):
- draws.append(bot[t] + (top[t] - bot[t])*RNG.rand(N))
- return draws
-
-def drawBernoulli(N,p=0.5,seed=0):
- '''
- Generates arrays of booleans drawn from a simple Bernoulli distribution.
- The input p can be a float or a list-like of floats; its length T determines
- the number of entries in the output. The t-th entry of the output is an
- array of N booleans which are True with probability p[t] and False otherwise.
-
- Arguments
- ---------
- N : int
- Number of draws in each row.
- p : float or [float]
- Probability or probabilities of the event occurring (True).
- seed : int
- Seed for random number generator.
-
- Returns
- -------
- draws : np.array or [np.array]
- T-length list of arrays of Bernoulli draws each of size N, or a single
- array of size N (if sigma is a scalar).
- '''
- # Set up the RNG
- RNG = np.random.RandomState(seed)
-
- if isinstance(p,float):# Return a single array of size N
- draws = RNG.uniform(size=N) < p
- else: # Set up empty list to populate, then loop and populate list with draws:
- draws=[]
- for t in range(len(p)):
- draws.append(RNG.uniform(size=N) < p[t])
- return draws
-
-
-def main():
- print("Sorry, HARK.simulation doesn't actually do anything on its own.")
- print("To see some examples of its functions in action, look at any")
- print("of the model modules in /ConsumptionSavingModel. In the future, running")
- print("this module will show examples of each function in the module.")
-
-if __name__ == '__main__':
- main()
diff --git a/HARK/tests/test_core.py b/HARK/tests/test_core.py
index e32fc0517..2fe91c96f 100644
--- a/HARK/tests/test_core.py
+++ b/HARK/tests/test_core.py
@@ -80,23 +80,6 @@ class testAgentType(unittest.TestCase):
def setUp(self):
self.agent = AgentType()
- def test_time(self):
- self.agent.time_vary = ['var_1', 'var_2']
- self.agent.var_1 = [4.3, 2, 1]
- self.agent.var_2 = [1, 2, 3, 4, 5]
- self.agent.timeFlip()
- self.assertEqual(self.agent.var_1, [1, 2, 4.3])
- self.assertEqual(self.agent.var_2, [5, 4, 3, 2, 1])
- self.assertEqual(self.agent.time_flow, False)
- self.agent.timeFlip()
- self.assertEqual(self.agent.var_1, [4.3, 2, 1])
- self.assertEqual(self.agent.var_2, [1, 2, 3, 4, 5])
- self.assertEqual(self.agent.time_flow, True)
- self.agent.timeRev()
- self.assertEqual(self.agent.time_flow, False)
- self.agent.timeFwd()
- self.assertEqual(self.agent.time_flow, True)
-
def test_solve(self):
self.agent.time_vary = ['vary_1']
self.agent.time_inv = ['inv_1']
@@ -107,4 +90,4 @@ def test_solve(self):
self.agent.solveOnePeriod = lambda vary_1: HARKobject()
self.agent.solve()
self.assertEqual(len(self.agent.solution), 4)
- self.assertTrue(isinstance(self.agent.solution[0], HARKobject))
\ No newline at end of file
+ self.assertTrue(isinstance(self.agent.solution[0], HARKobject))
diff --git a/HARK/tests/test_distribution.py b/HARK/tests/test_distribution.py
index c23eda75e..c8b27aa54 100644
--- a/HARK/tests/test_distribution.py
+++ b/HARK/tests/test_distribution.py
@@ -3,7 +3,7 @@
import HARK.distribution as distribution
-class DistributionTests(unittest.TestCase):
+class DiscreteDistributionTests(unittest.TestCase):
'''
Tests for simulation.py sampling distributions
with default seed.
@@ -17,3 +17,39 @@ def test_drawDiscrete(self):
).drawDiscrete(1)[0],
0)
+
+class DistributionClassTests(unittest.TestCase):
+ '''
+ Tests for simulation.py sampling distributions
+ with default seed.
+ '''
+
+ def test_drawMeanOneLognormal(self):
+ self.assertEqual(
+ distribution.drawMeanOneLognormal(1)[0],
+ 3.5397367004222002)
+
+ def test_Lognormal(self):
+ self.assertEqual(
+ distribution.Lognormal().draw(1)[0],
+ 5.836039190663969)
+
+ def test_Normal(self):
+ self.assertEqual(
+ distribution.Normal().draw(1)[0],
+ 1.764052345967664)
+
+ def test_Weibull(self):
+ self.assertEqual(
+ distribution.Weibull().draw(1)[0],
+ 0.79587450816311)
+
+ def test_Uniform(self):
+ self.assertEqual(
+ distribution.Uniform().draw(1)[0],
+ 0.5488135039273248)
+
+ def test_Bernoulli(self):
+ self.assertEqual(
+ distribution.Bernoulli().draw(1)[0],
+ False)
diff --git a/HARK/tests/test_simulation.py b/HARK/tests/test_simulation.py
index 3466d00ea..70fbba059 100644
--- a/HARK/tests/test_simulation.py
+++ b/HARK/tests/test_simulation.py
@@ -2,38 +2,3 @@
import HARK.simulation as simulation
-class SimulationTests(unittest.TestCase):
- '''
- Tests for simulation.py sampling distributions
- with default seed.
- '''
-
- def test_drawMeanOneLognormal(self):
- self.assertEqual(
- simulation.drawMeanOneLognormal(1)[0],
- 3.5397367004222002)
-
- def test_drawLognormal(self):
- self.assertEqual(
- simulation.drawLognormal(1)[0],
- 5.836039190663969)
-
- def test_drawNormal(self):
- self.assertEqual(
- simulation.drawNormal(1)[0],
- 1.764052345967664)
-
- def test_drawWeibull(self):
- self.assertEqual(
- simulation.drawWeibull(1)[0],
- 0.79587450816311)
-
- def test_drawUniform(self):
- self.assertEqual(
- simulation.drawUniform(1)[0],
- 0.5488135039273248)
-
- def test_drawBernoulli(self):
- self.assertEqual(
- simulation.drawBernoulli(1)[0],
- False)
diff --git a/examples/ConsumptionSaving/example_ConsMarkovModel.ipynb b/examples/ConsumptionSaving/example_ConsMarkovModel.ipynb
index 17f0eee6f..5c437bd93 100644
--- a/examples/ConsumptionSaving/example_ConsMarkovModel.ipynb
+++ b/examples/ConsumptionSaving/example_ConsMarkovModel.ipynb
@@ -12,6 +12,7 @@
"import numpy as np\n",
"from HARK.ConsumptionSaving.ConsIndShockModel import init_idiosyncratic_shocks\n",
"from HARK.ConsumptionSaving.ConsMarkovModel import MarkovConsumerType\n",
+ "from HARK.distribution import DiscreteDistribution\n",
"mystr = lambda number: \"{:.4f}\".format(number)\n",
"do_simulation = True"
]
@@ -65,7 +66,11 @@
{
"cell_type": "code",
"execution_count": 3,
- "metadata": {},
+ "metadata": {
+ "jupyter": {
+ "source_hidden": true
+ }
+ },
"outputs": [],
"source": [
"# Make a consumer with serially correlated unemployment, subject to boom and bust cycles\n",
@@ -85,8 +90,8 @@
"outputs": [],
"source": [
"# Replace the default (lognormal) income distribution with a custom one\n",
- "employed_income_dist = [np.ones(1), np.ones(1), np.ones(1)] # Definitely get income\n",
- "unemployed_income_dist = [np.ones(1), np.ones(1), np.zeros(1)] # Definitely don't\n",
+ "employed_income_dist = DiscreteDistribution(np.ones(1), [np.ones(1), np.ones(1)]) # Definitely get income\n",
+ "unemployed_income_dist = DiscreteDistribution(np.ones(1), [np.ones(1), np.zeros(1)]) # Definitely don't\n",
"SerialUnemploymentExample.IncomeDstn = [\n",
" [\n",
" employed_income_dist,\n",
@@ -120,7 +125,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "Solving a Markov consumer with serially correlated unemployment took 0.2911 seconds.\n",
+ "Solving a Markov consumer with serially correlated unemployment took 0.2833 seconds.\n",
"Consumption functions for each discrete state:\n"
]
},
@@ -190,16 +195,16 @@
"outputs": [],
"source": [
"StateCount = ImmunityT + 1 # Total number of Markov states\n",
- "IncomeDstnReg = [\n",
+ "IncomeDstnReg = DiscreteDistribution(\n",
" np.array([1 - UnempPrb, UnempPrb]),\n",
- " np.array([1.0, 1.0]),\n",
- " np.array([1.0 / (1.0 - UnempPrb), 0.0]),\n",
- "] # Ordinary income distribution\n",
- "IncomeDstnImm = [\n",
- " np.array([1.0]),\n",
+ " [np.array([1.0, 1.0]),\n",
+ " np.array([1.0 / (1.0 - UnempPrb), 0.0])]\n",
+ ") # Ordinary income distribution\n",
+ "IncomeDstnImm = DiscreteDistribution(\n",
" np.array([1.0]),\n",
- " np.array([1.0]),\n",
- "] # Income distribution when unemployed\n",
+ " [np.array([1.0]),\n",
+ " np.array([1.0])]\n",
+ ")\n",
"IncomeDstn = [IncomeDstnReg] + ImmunityT * [\n",
" IncomeDstnImm\n",
"] # Income distribution for each Markov state, in a list"
@@ -260,7 +265,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "Solving an \"unemployment immunity\" consumer took 0.3454 seconds.\n",
+ "Solving an \"unemployment immunity\" consumer took 0.3062 seconds.\n",
"Consumption functions for each discrete state:\n"
]
},
@@ -320,11 +325,11 @@
"metadata": {},
"outputs": [],
"source": [
- "IncomeDstnReg = [\n",
+ "IncomeDstnReg = DiscreteDistribution(\n",
" np.array([1 - UnempPrb, UnempPrb]),\n",
- " np.array([1.0, 1.0]),\n",
- " np.array([1.0, 0.0]),\n",
- "]\n",
+ " [np.array([1.0, 1.0]),\n",
+ " np.array([1.0, 0.0])]\n",
+ ")\n",
"IncomeDstn = StateCount * [\n",
" IncomeDstnReg\n",
"] # Same simple income distribution in each state"
@@ -375,7 +380,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "Solving a serially correlated growth consumer took 0.2647 seconds.\n",
+ "Solving a serially correlated growth consumer took 0.2594 seconds.\n",
"Consumption functions for each discrete state:\n"
]
},
@@ -431,7 +436,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "Solving a serially correlated interest consumer took 0.2409 seconds.\n",
+ "Solving a serially correlated interest consumer took 0.2642 seconds.\n",
"Consumption functions for each discrete state:\n"
]
},
diff --git a/examples/ConsumptionSaving/example_ConsMarkovModel.py b/examples/ConsumptionSaving/example_ConsMarkovModel.py
index ffc0a4e3e..512dca895 100644
--- a/examples/ConsumptionSaving/example_ConsMarkovModel.py
+++ b/examples/ConsumptionSaving/example_ConsMarkovModel.py
@@ -5,6 +5,7 @@
import numpy as np
from HARK.ConsumptionSaving.ConsIndShockModel import init_idiosyncratic_shocks
from HARK.ConsumptionSaving.ConsMarkovModel import MarkovConsumerType
+from HARK.distribution import DiscreteDistribution
mystr = lambda number: "{:.4f}".format(number)
do_simulation = True
@@ -60,8 +61,8 @@
# %%
# Replace the default (lognormal) income distribution with a custom one
-employed_income_dist = [np.ones(1), np.ones(1), np.ones(1)] # Definitely get income
-unemployed_income_dist = [np.ones(1), np.ones(1), np.zeros(1)] # Definitely don't
+employed_income_dist = DiscreteDistribution(np.ones(1), [np.ones(1), np.ones(1)]) # Definitely get income
+unemployed_income_dist = DiscreteDistribution(np.ones(1), [np.ones(1), np.zeros(1)]) # Definitely don't
SerialUnemploymentExample.IncomeDstn = [
[
employed_income_dist,
@@ -114,16 +115,16 @@
# %%
StateCount = ImmunityT + 1 # Total number of Markov states
-IncomeDstnReg = [
+IncomeDstnReg = DiscreteDistribution(
np.array([1 - UnempPrb, UnempPrb]),
- np.array([1.0, 1.0]),
- np.array([1.0 / (1.0 - UnempPrb), 0.0]),
-] # Ordinary income distribution
-IncomeDstnImm = [
+ [np.array([1.0, 1.0]),
+ np.array([1.0 / (1.0 - UnempPrb), 0.0])]
+) # Ordinary income distribution
+IncomeDstnImm = DiscreteDistribution(
np.array([1.0]),
- np.array([1.0]),
- np.array([1.0]),
-] # Income distribution when unemployed
+ [np.array([1.0]),
+ np.array([1.0])]
+)
IncomeDstn = [IncomeDstnReg] + ImmunityT * [
IncomeDstnImm
] # Income distribution for each Markov state, in a list
@@ -185,11 +186,11 @@
) # Probability of getting the same permanent income growth rate next period
# %%
-IncomeDstnReg = [
+IncomeDstnReg = DiscreteDistribution(
np.array([1 - UnempPrb, UnempPrb]),
- np.array([1.0, 1.0]),
- np.array([1.0, 0.0]),
-]
+ [np.array([1.0, 1.0]),
+ np.array([1.0, 0.0])]
+)
IncomeDstn = StateCount * [
IncomeDstnReg
] # Same simple income distribution in each state
diff --git a/examples/FashionVictim/FashionVictimModel.py b/examples/FashionVictim/FashionVictimModel.py
index 8b921ac80..d8a1794f3 100644
--- a/examples/FashionVictim/FashionVictimModel.py
+++ b/examples/FashionVictim/FashionVictimModel.py
@@ -137,7 +137,7 @@ def __init__(self,**kwds):
new instance of FashionVictimType
'''
# Initialize a basic AgentType
- AgentType.__init__(self,solution_terminal=FashionVictimType._solution_terminal,cycles=0,time_flow=True,pseudo_terminal=True,**kwds)
+ AgentType.__init__(self,solution_terminal=FashionVictimType._solution_terminal,cycles=0,pseudo_terminal=True,**kwds)
# Add class-specific features
self.time_inv = ['DiscFac','conformUtilityFunc','punk_utility','jock_utility','switchcost_J2P','switchcost_P2J','pGrid','pEvolution','pref_shock_mag']
diff --git a/examples/GenIncProcessModel/GenIncProcessModel.ipynb.orig b/examples/GenIncProcessModel/GenIncProcessModel.ipynb.orig
new file mode 100644
index 000000000..44a3ff9e0
--- /dev/null
+++ b/examples/GenIncProcessModel/GenIncProcessModel.ipynb.orig
@@ -0,0 +1,702 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Permanent versus Persistent Income Shocks\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "code_folding": []
+ },
+ "outputs": [],
+ "source": [
+ "# Initial imports and notebook setup\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "import sys\n",
+ "import os\n",
+ "from copy import copy\n",
+ "from HARK.utilities import plotFuncs\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from HARK.ConsumptionSaving.ConsGenIncProcessModel import *\n",
+ "from HARK.ConsumptionSaving.ConsIndShockModel import IndShockConsumerType\n",
+ "import HARK.ConsumptionSaving.ConsumerParameters as Params"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`ConsIndShockModel` assumes that income has a permanent component $p$ which is subject to \"permanent\" shocks:\n",
+ "\n",
+ " $\\log p_{t+1} = \\log p_{t} + \\log \\psi_{t+1}$\n",
+ "\n",
+ "Many papers in the literature instead examine models in which shocks merely have some persistence,\n",
+ "\n",
+ "$\\log p_{t+1} = \\gamma \\log p_{t} + \\log \\psi_{t+1}$\n",
+ "\n",
+ "where if $0 < \\gamma < 1$ then $\\lim_{n \\uparrow \\infty} \\mathbb{E}_{t}[\\log p_{t+n}]=0$ (which means that the level of $p$ reverts to its mean of $p=1$. The two models become identical as $\\gamma$ approaches 1.\n",
+ "\n",
+ "This notebook describes HARK's tools to solve models with persistent shocks.\n",
+ "\n",
+ "1. `ConsGenIncProcessModel` extends `ConsIndShockModel` by explicitly tracking persistent income $p_t$ as a state variable.\n",
+ "1. `IndShockExplicitPermIncConsumerType` is a type of consumer created for comparison and for whom we know for sure that their income process is one in which $\\gamma=1$\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "## General Income Process model\n",
+ "In `ConsGenIncProcessModel` the user can define a generic function $G$ that translates current $p_{t}$ into expected next period persistent income $p_{t+1}$ (subject to shocks). \n",
+ "\n",
+ "\n",
+ "The agent's problem can be written in Bellman form as:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\\begin{eqnarray*}\n",
+ "v_t(M_t,p_t) &=& \\max_{c_t} U(c_t) + \\beta (1-\\mathsf{D}_{t+1}) \\mathbb{E}_{t} [v_{t+1}(M_{t+1}, p_{t+1})] \\\\\n",
+ "a_t &=& M_t - c_t \\\\\n",
+ "a_t &\\geq& \\underline{a} \\\\\n",
+ "M_{t+1} &=& R a_t + \\theta_{t+1} \\\\\n",
+ "p_{t+1} &=& G_{t+1}(p_t)\\psi_{t+1} \\\\\n",
+ "\\psi_t \\sim F_{\\psi t} &\\qquad& \\theta_t \\sim F_{\\theta t} \\\\\n",
+ " \\mathbb{E} [F_{\\psi t}] = 1 & & \\mathbb{E} [F_{\\psi t}] =1 \\\\\n",
+ "U(c) &=& \\frac{c^{1-\\rho}}{1-\\rho}\n",
+ "\\end{eqnarray*}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The one-period problem for this model is solved by the function $\\texttt{solveConsGenIncProcess}$, which creates an instance of the class $\\texttt{ConsGenIncProcessSolver}$. The class $\\texttt{GenIncProcessConsumerType}$ extends $\\texttt{IndShockConsumerType}$ to represent agents in this model. To construct an instance of this class, several parameters must be passed to the constructor, as shown in the table below (parameters can be either \"primitive\" or \"constructed\" if they have already built-in capabilities from previous models).\n",
+ "\n",
+ "### Example parameter values to solve GenIncProcess model\n",
+ "\n",
+ "| Parameter | Description | Code | Value | Constructed |\n",
+ "| :---: | --- | --- | --- | :---: |\n",
+ "| $\\beta$ |Intertemporal discount factor | $\\texttt{DiscFac}$ | 0.96 | |\n",
+<<<<<<< HEAD
+ "| $\\rho$ |Coefficient of relative risk aversion | $\\texttt{CRRA}$ | 2.0 | |\n",
+ "| $R$ | Risk free interest factor | $\\texttt{Rfree}$ | 1.03 | |\n",
+ "| $1 - \\mathsf{D}$ |Survival probability | $\\texttt{LivPrb}$ | [0.98] | |\n",
+ "| $\\underline{a}$ |Artificial borrowing constraint | $\\texttt{BoroCnstArt}$ | 0.0 | | \n",
+ "| $(none)$ |Indicator of whether $\\texttt{vFunc}$ should be computed | $\\texttt{vFuncBool}$ | 'True' | |\n",
+ "| $(none)$ |Indicator of whether $\\texttt{cFunc}$ should use cubic lines | $\\texttt{CubicBool}$ | 'False' | |\n",
+ "|$F$ |A list containing three arrays of floats, representing a discrete approximation to the income process: event probabilities, persistent shocks, transitory shocks | $\\texttt{IncomeDstn}$ | - |$\\surd$ |\n",
+ "| $G$ |Expected persistent income next period | $\\texttt{pLvlNextFunc}$ | - | $\\surd$ |\n",
+ "| $(none)$ |Array of time-varying persistent income levels | $\\texttt{pLvlGrid}$ | - |$\\surd$ |\n",
+ "| $(none)$ | Array of \"extra\" end-of-period asset values | $\\texttt{aXtraGrid}$ | - |$\\surd$ |\n",
+=======
+ "| $\\rho$|Coefficient of relative risk aversion | $\\texttt{CRRA}$ | 2.0 | |\n",
+ "| $R$| Risk free interest factor | $\\texttt{Rfree}$ | 1.03 | |\n",
+ "| $1 - \\mathsf{D}$ |Survival probability | $\\texttt{LivPrb}$ | [0.98] | |\n",
+ "| $\\underline{a}$|Artificial borrowing constraint | $\\texttt{BoroCnstArt}$ | 0.0 | | \n",
+ "| $(none)~$|Indicator of whether $\\texttt{vFunc}$ should be computed | $\\texttt{vFuncBool}$ | 'True' | |\n",
+ "| $(none)$ |Indicator of whether $\\texttt{cFunc}$ should use cubic lines | $\\texttt{CubicBool}$ | 'False' | |\n",
+ "|$F$|A list containing three arrays of floats, representing a discrete approximation to the income process: event probabilities, persistent shocks, transitory shocks | $\\texttt{IncomeDstn}$ | - |$\\surd$ |\n",
+ "| $G$ |Expected persistent income next period | $\\texttt{pLvlNextFunc}$ | - | $\\surd$ |\n",
+ "|$(none)$|Array of time-varying persistent income levels | $\\texttt{pLvlGrid}$ | - |$\\surd$ |\n",
+ "|$(none)$| Array of \"extra\" end-of-period asset values | $\\texttt{aXtraGrid}$ | - |$\\surd$ |\n",
+>>>>>>> master
+ "\n",
+ "### Constructed inputs to solve GenIncProcess\n",
+ "The \"constructed\" inputs above are using expected attributes and are drawn on various methods as explained below.\n",
+ "\n",
+ "\n",
+ "* The input $\\texttt{IncomeDstn}$ is created by the method $\\texttt{updateIncomeProcess}$ which inherits from $\\texttt{IndShockConsumerType}$. (*hyperlink to that noteboook*)\n",
+ "\n",
+ "* The input $\\texttt{pLvlNextFunc}$ is created by the method $\\texttt{updatepLvlNextFunc}$ which uses the initial sequence of $\\texttt{pLvlNextFunc}$, the mean and standard deviation of the (log) initial permanent income, $\\texttt{pLvlInitMean}$ and $\\texttt{pLvlInitStd}$. \n",
+ "In this model, the method creates a trivial $\\texttt{pLvlNextFunc}$ attribute with no persistent income dynamics. But we can overwrite it by subclasses in order to make an AR1 income process for example. \n",
+ "\n",
+ "\n",
+ "* The input $\\texttt{pLvlGrid}$ is created by the method $\\texttt{updatepLvlGrid}$ which updates the grid of persistent income levels for infinite horizon models (cycles=0) and lifecycle models (cycles=1). This method draws on the initial distribution of persistent income, the $\\texttt{pLvlNextFuncs}$, $\\texttt{pLvlInitMean}$, $\\texttt{pLvlInitStd}$ and the attribute $\\texttt{pLvlPctiles}$ (percentiles of the distribution of persistent income). It then uses a simulation approach to generate the $\\texttt{pLvlGrid}$ at each period of the cycle.\n",
+ "\n",
+ "\n",
+ "* The input $\\texttt{aXtraGrid}$ is created by $\\texttt{updateAssetsGrid}$ which updates the agent's end-of-period assets grid by constructing a multi-exponentially spaced grid of aXtra values, based on $\\texttt{aNrmInitMean}$ and $\\texttt{aNrmInitStd}$. \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Consumer with Explicit Permanent Income\n",
+ "\n",
+ "Let's make an example of our generic model above with an \"explicit permanent income\" consumer who experiences idiosyncratic shocks to permanent and transitory, and faces permanent income growth.\n",
+ "\n",
+ "The agent's problem can be written in Bellman form as:\n",
+ "\n",
+ "\\begin{eqnarray*}\n",
+ "v_t(M_t,p_t) &=& \\max_{c_t} U(c_t) + \\beta (1-\\mathsf{D}_{t+1}) \\mathbb{E} [v_{t+1}(M_{t+1}, p_{t+1}) ], \\\\\n",
+ "a_t &=& M_t - c_t, \\\\\n",
+ "a_t &\\geq& \\underline{a}, \\\\\n",
+ "M_{t+1} &=& R/(\\Gamma_{t+1} \\psi_{t+1}) a_t + \\theta_{t+1}, \\\\\n",
+ "p_{t+1} &=& G_{t+1}(p_t)\\psi_{t+1}, \\\\\n",
+ "\\psi \\sim F_{\\psi}, \\mathbb{E} [F_{\\psi t}] = 1 &\\qquad& \\theta_t \\sim F_{\\theta}, \\mathbb{E} [F_{\\psi}] = 1, \\\\\n",
+ "U(c) &=& \\frac{c^{1-\\rho}}{1-\\rho}.\n",
+ "\\end{eqnarray*}\n",
+ "\n",
+ "\n",
+ "This agent type is identical to an $\\texttt{IndShockConsumerType}$ but for explicitly tracking $\\texttt{pLvl}$ as a state variable during solution as shown in the mathematical representation of GenIncProcess model. \n",
+ "\n",
+ "To construct $\\texttt{IndShockExplicitPermIncConsumerType}$ as an instance of $\\texttt{GenIncProcessConsumerType}$, we need to pass additional parameters to the constructor as shown in the table below.\n",
+ "\n",
+ "### Additional parameters to solve ExplicitPermInc model\n",
+ "\n",
+ "| Param | Description | Code | Value | Constructed |\n",
+ "| :---: | --- | --- | --- | :---: |\n",
+ "|(none)|percentiles of the distribution of persistent income|$\\texttt{pLvlPctiles}$|||\n",
+ "| $G$ |Expected persistent income next period | $\\texttt{pLvlNextFunc}$ | - | $\\surd$ |\n",
+ "|$\\Gamma$|Permanent income growth factor|$\\texttt{PermGroFac}$|[1.0]| |\n",
+ "\n",
+ "\n",
+ "### Constructed inputs to solve ExplicitPermInc\n",
+ "\n",
+ "* In this \"explicit permanent income\" model, we overwrite the method $\\texttt{updatepLvlNextFunc}$ to create $\\texttt{pLvlNextFunc}$ as a sequence of linear functions, indicating constant expected permanent income growth across permanent income levels. This method uses the attribute $\\texttt{PermGroFac}$, and installs a special retirement function when it exists.\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "code_folding": []
+ },
+ "outputs": [],
+ "source": [
+ "# This cell defines a dictionary to make an instance of \"explicit permanent income\" consumer.\n",
+ "GenIncDictionary = { \n",
+ " \"CRRA\": 2.0, # Coefficient of relative risk aversion\n",
+ " \"Rfree\": 1.03, # Interest factor on assets\n",
+ " \"DiscFac\": 0.96, # Intertemporal discount factor\n",
+ " \"LivPrb\" : [0.98], # Survival probability\n",
+ " \"AgentCount\" : 10000, # Number of agents of this type (only matters for simulation)\n",
+ " \"aNrmInitMean\" : 0.0, # Mean of log initial assets (only matters for simulation)\n",
+ " \"aNrmInitStd\" : 1.0, # Standard deviation of log initial assets (only for simulation)\n",
+ " \"pLvlInitMean\" : 0.0, # Mean of log initial permanent income (only matters for simulation)\n",
+ " \"pLvlInitStd\" : 0.0, # Standard deviation of log initial permanent income (only matters for simulation)\n",
+ " \"PermGroFacAgg\" : 1.0, # Aggregate permanent income growth factor (only matters for simulation)\n",
+ " \"T_age\" : None, # Age after which simulated agents are automatically killed\n",
+ " \"T_cycle\" : 1, # Number of periods in the cycle for this agent type\n",
+ "# Parameters for constructing the \"assets above minimum\" grid\n",
+ " \"aXtraMin\" : 0.001, # Minimum end-of-period \"assets above minimum\" value\n",
+ " \"aXtraMax\" : 30, # Maximum end-of-period \"assets above minimum\" value \n",
+ " \"aXtraExtra\" : [0.005,0.01], # Some other value of \"assets above minimum\" to add to the grid\n",
+ " \"aXtraNestFac\" : 3, # Exponential nesting factor when constructing \"assets above minimum\" grid\n",
+ " \"aXtraCount\" : 48, # Number of points in the grid of \"assets above minimum\"\n",
+ "# Parameters describing the income process\n",
+ " \"PermShkCount\" : 7, # Number of points in discrete approximation to permanent income shocks\n",
+ " \"TranShkCount\" : 7, # Number of points in discrete approximation to transitory income shocks\n",
+ " \"PermShkStd\" : [0.1], # Standard deviation of log permanent income shocks\n",
+ " \"TranShkStd\" : [0.1], # Standard deviation of log transitory income shocks\n",
+ " \"UnempPrb\" : 0.05, # Probability of unemployment while working\n",
+ " \"UnempPrbRet\" : 0.005, # Probability of \"unemployment\" while retired\n",
+ " \"IncUnemp\" : 0.3, # Unemployment benefits replacement rate\n",
+ " \"IncUnempRet\" : 0.0, # \"Unemployment\" benefits when retired\n",
+ " \"tax_rate\" : 0.0, # Flat income tax rate\n",
+ " \"T_retire\" : 0, # Period of retirement (0 --> no retirement)\n",
+ " \"BoroCnstArt\" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets\n",
+ " \"CubicBool\" : False, # Use cubic spline interpolation when True, linear interpolation when False\n",
+ " \"vFuncBool\" : True, # Whether to calculate the value function during solution \n",
+ "# More parameters specific to \"Explicit Permanent income\" shock model\n",
+ " \"cycles\": 0,\n",
+ " \"pLvlPctiles\" : np.concatenate(([0.001, 0.005, 0.01, 0.03], np.linspace(0.05, 0.95, num=19),[0.97, 0.99, 0.995, 0.999])),\n",
+ " \"PermGroFac\" : [1.0], # Permanent income growth factor - long run permanent income growth doesn't work yet \n",
+ "}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's now create an instance of the type of consumer we are interested in and solve this agent's problem with an infinite horizon (cycles=0)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Here, the lowest percentile is 0.1\n",
+ "and the highest percentile is 99.9.\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Make and solve an example \"explicit permanent income\" consumer with idiosyncratic shocks\n",
+ "ExplicitExample = IndShockExplicitPermIncConsumerType(**GenIncDictionary)\n",
+ " \n",
+ "print('Here, the lowest percentile is ' + str(GenIncDictionary['pLvlPctiles'][0]*100))\n",
+ "print('and the highest percentile is ' + str(GenIncDictionary['pLvlPctiles'][-1]*100) + '.\\n')\n",
+ " \n",
+ "ExplicitExample.solve()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In the cell below, we generate a plot of the consumption function for explicit permanent income consumer at different income levels."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "code_folding": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Consumption function by pLvl for explicit permanent income consumer:\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot the consumption function at various permanent income levels.\n",
+ "print('Consumption function by pLvl for explicit permanent income consumer:')\n",
+ "pLvlGrid = ExplicitExample.pLvlGrid[0]\n",
+ "mLvlGrid = np.linspace(0,20,300)\n",
+ "for p in pLvlGrid:\n",
+ " M_temp = mLvlGrid + ExplicitExample.solution[0].mLvlMin(p)\n",
+ " C = ExplicitExample.solution[0].cFunc(M_temp,p*np.ones_like(M_temp))\n",
+ " plt.plot(M_temp,C)\n",
+ "plt.xlim(0.,20.)\n",
+ "plt.xlabel('Market resource level mLvl')\n",
+ "plt.ylabel('Consumption level cLvl')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Permanent income normalized\n",
+ "\n",
+ "An alternative model is to normalize it by dividing all variables by permanent income $p_t$ and solve the model again."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "The given parameter values violate the Individual Growth Impatience Condition; the GIFInd is: 1.0037 \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Make and solve an example of normalized model\n",
+ "NormalizedExample = IndShockConsumerType(**GenIncDictionary)\n",
+ "NormalizedExample.solve()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Normalized consumption function by pLvl for explicit permanent income consumer:\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Consumption function for normalized problem (without explicit permanent income):\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Compare the normalized problem with and without explicit permanent income and plot the consumption functions\n",
+ "print('Normalized consumption function by pLvl for explicit permanent income consumer:')\n",
+ "pLvlGrid = ExplicitExample.pLvlGrid[0]\n",
+ "mNrmGrid = np.linspace(0,20,300)\n",
+ "for p in pLvlGrid:\n",
+ " M_temp = mNrmGrid*p + ExplicitExample.solution[0].mLvlMin(p)\n",
+ " C = ExplicitExample.solution[0].cFunc(M_temp,p*np.ones_like(M_temp))\n",
+ " plt.plot(M_temp/p,C/p)\n",
+ "\n",
+ "plt.xlim(0.,20.)\n",
+ "plt.xlabel('Normalized market resources mNrm')\n",
+ "plt.ylabel('Normalized consumption cNrm')\n",
+ "plt.show()\n",
+ "\n",
+ "print('Consumption function for normalized problem (without explicit permanent income):')\n",
+ "mNrmMin = NormalizedExample.solution[0].mNrmMin\n",
+ "plotFuncs(NormalizedExample.solution[0].cFunc,mNrmMin,mNrmMin+20.)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The figures above show that the normalized consumption function for the \"explicit permanent income\" consumer is almost identical for every permanent income level (and the same as the normalized problem's $\\texttt{cFunc}$), but is less accurate due to extrapolation outside the bounds of $\\texttt{pLvlGrid}$. \n",
+ "\n",
+ "The \"explicit permanent income\" solution deviates from the solution to the normalized problem because of errors from extrapolating beyond the bounds of the $\\texttt{pLvlGrid}$. The error is largest for $\\texttt{pLvl}$ values near the upper and lower bounds, and propagates toward the center of the distribution.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot the value function at various permanent income levels\n",
+ "if ExplicitExample.vFuncBool:\n",
+ " pGrid = np.linspace(0.1,3.0,24)\n",
+ " M = np.linspace(0.001,5,300)\n",
+ " for p in pGrid:\n",
+ " M_temp = M+ExplicitExample.solution[0].mLvlMin(p)\n",
+ " C = ExplicitExample.solution[0].vFunc(M_temp,p*np.ones_like(M_temp))\n",
+ " plt.plot(M_temp,C)\n",
+ " plt.ylim([-200,0])\n",
+ " plt.xlabel('Market resource level mLvl')\n",
+ " plt.ylabel('Value v')\n",
+ " plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Simulate many periods to get to the stationary distribution\n",
+ "ExplicitExample.T_sim = 500\n",
+ "ExplicitExample.track_vars = ['mLvlNow','cLvlNow','pLvlNow']\n",
+ "ExplicitExample.initializeSim()\n",
+ "ExplicitExample.simulate()\n",
+ "plt.plot(np.mean(ExplicitExample.mLvlNow_hist,axis=1))\n",
+ "plt.xlabel('Simulated time period')\n",
+ "plt.ylabel('Average market resources mLvl')\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2. Persistent income shock consumer\n",
+ "\n",
+ "\n",
+ "Class to solve consumption-saving models with idiosyncratic shocks to income in which shocks are persistent and transitory. This model extends $\\texttt{ConsGenIndShockModel}$ by allowing (log) persistent income to follow an AR(1) process.\n",
+ "\n",
+ "The agent's problem can be written in Bellman form as:\n",
+ "\n",
+ "\\begin{eqnarray*}\n",
+ "v_t(M_t,p_t) &=& \\max_{c_t} U(c_t) + \\beta (1-\\mathsf{D}_{t+1}) \\mathbb{E} [v_{t+1}(M_{t+1}, p_{t+1}) ], \\\\\n",
+ "a_t &=& M_t - c_t, \\\\\n",
+ "a_t &\\geq& \\underline{a}, \\\\\n",
+ "M_{t+1} &=& R a_t + \\theta_{t+1}, \\\\\n",
+ "log(p_{t+1}) &=& \\varphi log(p_t)+(1-\\varphi log(\\overline{p}_{t+1} ) +log(\\Gamma_{t+1})+log(\\psi_{t+1}), \\\\\n",
+ "\\\\\n",
+ "\\psi_t \\sim F_{\\psi t} &\\qquad& \\theta_t \\sim F_{\\theta t}, \\mathbb{E} [F_{\\psi t}] = 1 \\\\\n",
+ "\\end{eqnarray*}\n",
+ "\n",
+ "### Additional parameters to solve PersistentShock model\n",
+ "\n",
+ "| Param | Description | Code | Value | Constructed |\n",
+ "| :---: | --- | --- | --- | :---: |\n",
+ "|$\\varphi$|Serial correlation coefficient for permanent income|$\\texttt{PrstIncCorr}$|0.98||\n",
+ "||||||\n",
+ "\n",
+ "### Constructed inputs to solve PersistentShock\n",
+ "\n",
+ "* For this model, we overwrite the method $\\texttt{updatepLvlNextFunc}$ to create the input $\\texttt{pLvlNextFunc}$ as a sequence of AR1-style functions. The method uses now the attributes $\\texttt{PermGroFac}$ and $\\texttt{PrstIncCorr}$. If cycles=0, the product of $\\texttt{PermGroFac}$ across all periods must be 1.0, otherwise this method is invalid.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "code_folding": []
+ },
+ "outputs": [],
+ "source": [
+ "# Make a dictionary for the \"persistent idiosyncratic shocks\" model\n",
+ "PrstIncCorr = 0.98 # Serial correlation coefficient for persistent income\n",
+ "\n",
+ "persistent_shocks = copy(GenIncDictionary)\n",
+ "persistent_shocks['PrstIncCorr'] = PrstIncCorr\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The $\\texttt{PersistentShockConsumerType}$ class solves the problem of a consumer facing idiosyncratic shocks to his persistent and transitory income, and for which the (log) persistent income follows an AR1 process rather than random walk."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Make and solve an example of \"persistent idisyncratic shocks\" consumer\n",
+ "PersistentExample = PersistentShockConsumerType(**persistent_shocks)\n",
+ "PersistentExample.solve()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Consumption function by persistent income level pLvl for a consumer with AR1 coefficient of 0.98:\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEGCAYAAACZ0MnKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOy9eZCj+X3e93lx34376PsE0N1z7C5nLy7J5S5JiVyaou1dmpQsWYldYkVVTmI5dqVi2ZLlRLZcjlUlW0pZdDGJ5NiSGFrxIUeSZSkyJVGivORyd2e6G33fF4BGN+77lz/eF+8LzLHbczRmZud9qlDoGbwA3pkG8OD5Ps/3+5WEEOjQoUOHDh3ngeFhn4AOHTp06Hh8oJOGDh06dOg4N3TS0KFDhw4d54ZOGjp06NCh49zQSUOHDh06dJwbpod9AneLYDAoxsfHH/Zp6NChQ8djhW9/+9sZIUTofh/nsSON8fFx3nzzzYd9Gjp06NDxWEGSpK0H8Th6eUqHDh06dJwbOmno0KFDh45zQycNHTp06NBxbuikoUOHDh06zg2dNHTo0KFDx7mhk4YOHTp06Dg3dNLQoUOHDh3nxmPXp6FDhw4dOs6HVrFO47BM47D0wB5TJw0dOnToeMwhGm0axzI5NA5KNI5KNA5LtAuNB/5cOmno0KFDx2MC0Ra0clVVPXQuzUwFOvv0TAbMEQe2uB9z1IE56sQcdcI/fDDnoJOGDh06dDyCaJcbXcqhQxJlRL2lHmP02zBHndgvB2VyiDkxBexIBunCzksnDR06dOh4iBDNrtJSl4Jo5+vqMQaHCXPUifNaBFNHPUScGKzGvp+vTho6dOjQ0QcIIWid1ro8hzKNgxLNTBnaykFGCXPYgW3KqyoHc9SBwW1Bki5OPdwNdNLQoUOHjgeMdqXZ4zl0FISodZWWfFa5tDQfUHwHB6agHcn4aHdC6KShQ4cOHfcI0WzTzFQ070EhiNZZTT1GspkwRx04ngmrprQ54sBgezw/fh/Ps9ahQ4eOPkIIQeus3ptYOizRSFegpcSWjBLmkB3rhAdThxxiToyeR6e09CCgk4YOHTp0dKFda8meQ0c5HCippWpTPcY4YMUcc2JL+lX1YArakUyPdmnpQUAnDR06dDyREG1B66RK47BE/UBTEK1sVT1GshoxR504rmqRVnPEicH+5H50Prn/ch06dDwxkHseuhrilASTqCuxJQlMQTuWQRfmZyJKasmJ0Wf9QJWWHgR00tChQ8cHBqIlaGY64zS0sRrdxrTa8/BsVGuICzswWPrf8/A4QicNHTp0PJZoFes3+Q4lGsdlaCrGtEHCHJaN6Y5yMMecj1TPw+MInTR06NDxSEPtmO7yHRoHJdpFbRifwW3BHHPimvZpBBF6MozpfuPCSEOSJBvwDcCqPM/XhRA/edMxVuCXgQ8BWeCLQojNizonHTp0PLoQQtDK36oemumujmmThDnixJbwa+QQdWB0WR7quT9JuEilUQNeFUIUJUkyA38oSdJvCiH+pOuYvwLkhBDTkiR9CXkO4xcv8Jx06NDxCKBdb9E80tRDJ70kKl2xVq8ca7XPBVSCMAXsSEa9tPQwcWGkIYQQQFH5o1m5iJsO+zzwd5Wfvw78vCRJknJfHTp0PObQRnn3dkw3s9oob8lilDumr+ix1scBF/pbkSTJCHwbmAZ+QQjxrZsOGQJ2AIQQTUmSzoAAkLnpcb4MfBlgdHT0Ik9Zhw4d94h2tdlLDp2muM4obwlMAbtMEE+FumKttgsd5a0D6tXKA3usCyUNIUQLeEqSJC/w/0iSdEkIcb3rkNu9Um5RGUKIrwBfAbh27ZquQnToeIgQLUEzW7mFIFqnN81bismjvNVYa0SPtV402q0WuYN9MjubZLY3SW9vkdnZ5Ozo8IE9R1/0nxDiVJKk3wc+DXSTxi4wAuxKkmQCBoCTfpyTDh063h+tUuPWWOtRGZqKM20AU8iBZcyD+YUP7rylRw1CCEqnOTJbG6R3ttTrk70dWg05VSYZDPiig0Qmppl/+RPwtf/wQJ77ItNTIaChEIYd+CS3Lhz8d8APA38MvAH8nu5n6NDRf4hmm0b6VvXQLnQtAnKZ5VjrizHNewg79FjrBaNRrZLZ3SKzvUV6e0O53qRayKvHuHx+gqPjjF1+iuDIGMHRcQJDI5gs3amyH3gg53ORSiMG/JLiaxiArwkhfkOSpL8HvCmE+HfAV4F/IUnSKrLC+NIFno8OHTqAVkGJtR6UaBwUlaa4CrS7prVGHNhmvF2xVidGtx5rvUiIdpvT40MyW5uktzvlpQ1Ojw5B+S5tsloJjYwz8+wLBEcnCI3KBGF3e/p2ntLj9sX+2rVr4s0333zYp6FDxyMPdaTGgRJpPSjR2C/2NMUZByyKanBhjjm0aa2P+CKgxx3l/BkZxW9Ib23KHsTOFs2a4gtJEr7oIMHRMUKjE+r1QDiCZLi3340kSd8WQly733PXM206dHwA0C43NGJQvYeSNlKjs0Y07pMJYlBRD07zwz3xDziajQYnezuKathUr0s5zbq1uz2Exsa58ur3EhwbJzQyTmBkFLPV9hDP/M7QSUOHjscIoi1onlTlslIXSXQnlwzOjvcwiHnQhSXmxBTS1cNFQghBIZPuIYbM9iYn+7uIthwaMJpMBIbHGLv8FKHRcYKj44TGJnAMeB+r0IBOGjp0PKJo11qaMd0hicObxnmH7GpyyRKTy0wGt/mx+hB63FArl1Qzupsg6pWyeownFCE4Osb0sy+qpSVfbBCDsf+R41arzelh+f0PPCd00tCh4yFDXiVao7HfSxDNk6rWNW0zKn0PUdmcjsl7piWz3vdwUZB7HvY0ctjaILOzRT59rB5jdTgJjo4x+9FXFFN6guDIGFaHo+/nK8dwa2R2i5zsl8juFcnuFckdlmm3Hpx3rZOGDh19hGi0tVWiB3eYuRSwYYk6cTwdVv0Ho1dfBnRRUHsebvIdunseDEYjvtgQg/FZrnzi04TGZHPaHQg9lN9LvdIk20UM2T2ZKGpl7XXk8lkJDLkYuxTAP+iCX3wwz62Thg4dFwQt2lpUTeruia2S2SCvEr0clI3pmAtz1IHBqr8tLwqNWpXszvYtpaXKHXoeQmOycvAPjWAy9z800G61OT2qkN0vkt0tqkRR6FpJa7YZCQy6mL4WITDoJDDkwj/oxHZBIQf91alDx31CtNo00xVFOWgGdW+09aaJrTFlYqs+c+lCcLueh8zOJrnDg56eh+DIGNPPviCb0oo53c+eB/V8haB8VifTUQ17JbL7RU4OSrSVBJxkkPBGHEQnPMx9ZJDAkIvAkBO339ZXtaOThg4dd4F2pSkrh27/4agMrZsa4zr7HmKyQW1w6NHWi8L5eh5iBEfHSb70cUJjMjl4w9F77nm4H9SrTc1z2C8pCqJIraSVlpxeK4EhJyNJP4EhJ4FhF76IE6P54SfgdNLQoeM2kM3pOo39Io19pby0X6SV64q2dsZqvDSIOaZHWy8arWaTk/1dec6SYkw/yj0P7Vabs3SF7F6v95DPdJWWrEb8g06mng6ryiEw5Lqw0tKDgE4aOp54iJagmS6rxNDYl0tM7Y6pqIz0toy4MT8XwzzoxBJzYfToYzUuCuWzU463NnoIIru7Q7sl/06MJhP+4VHGLl1VTOmH2/NQztd7iCG7V+Jkv0RLGewoSeCNOAiPeZj9cAz/oIvgsEsuLT1mJUqdNHQ8UVB7H/aLNPYVD+Kwq3PaJGGOOrHPK+b0oG5OXyRazQYne7uqakhvbZDe2qB8dqoe4/L5CY5NMP7Uhwgp3oNvcBijqf+/k1ajzcmhohx2ZYLI7JWo5LXBjg6PhcCQk8sfH1LUgwtfzIHpAxKP1t8JOj6waBXq1BVyaBzI190b4wwOE+ZBl9Y5PejEFHTo60QvCKXTnEoK6e1NMlsbZPd2NfVgNhMYHmXiqWuExiZU78HhGej7uXb3PHSUQ6fnQSiDHY0mA/5BJ2OXAgS7Skv2D/hgR500dDz2EG1lKZBCDvX92wzm89swxzq9D7KCMA7oOx8uAp15Sz0Esb3Zqx4CQUKj40w83SGICXyxoYfSMd2otbRIa5f/0N3z4PbbCAy7mLgaJDAkl5YGQnYMT6B/pZOGjscKotmmcVSmsVdUVESxd7SGoTe9ZFH6H/R90w8eQghKuZOeslJn3lK7Ja94NZktBEbGmHzmWbm0pPgPDyXW2hbksxWyuyU12prdLXKW0dSn2WokMORk+kOKMT3sIjDoxKqn31To7yQdjyza9ZY6zru+pxBEV7xVshoxDyqjNTr+g74U6ELQrNfJKuohs60oiK3epjh3IERobJypa8+r5OCLPpx5S7VyQ1UNmT2tMa5Z0/aVe8MOgiMuEi9EVe/BE3j8jOl+QycNHY8E2tWmQg4aSTTTZc1/cMr+g/ujQ7L/MOTC6NPf4A8aQgiKuaxKCp2ZS93TWk0WK8GRUaUpboKwQhA2l6vv56t2THfIQSGIYlc02uo0ERxyMffhmKwchlz4Y07M1g+GMd1v6KSho+9olRq96mGvSLNrLILRY8E85MJ+OYhl0IV5SPcfLgKNeo2T3R2Ot9bVzun01gbVYkE9xhMKExqbYOa5F+VNcWMTeKNRDIb+f+D2xFp3ZZLIHZTVWKvBIOGNOohNewkq5BAYcuH0PtmvnXa9Tn1t7YE9nk4aOi4UrbySYNrTSKJ794PRb8My6MRxLSITxKBLXyv6gNEZyJfeXOe4Y05vbZDb30MIRT0oa0Tjz78kN8UpIzVszv6rh2ajRe6g3NP3cEusdcBCcMgld0wPy8mlR6Vj+mFBCEFjb5/a8jK15RS15WWqqWXqm5ugeEwPAjpp6HhgaJUa1HcLNHYK1HeL1PcKtAtKgkkCU1De/WD5sEuNuOrjNR4sOl3THWI43lwnvbVBJX+mHuMJRQiNTRB/4SOExmRz+mGM1JBLYbWb1EOJ06OuWKvZgD/25MVa3w+tfF4hhRS15RWFKJZpl0rqMeahIayJBO5PfRJbPA6f/ewDeW6dNHTcE9rVpqwcdhWC2C1oIzaU5UC2GR/mIdl/MMeceoPcA0a1WCS9ta6Qw4bSNb1Fq6n1PQRHxpj60HOExiZl72Hs4aiHerXJyUHpXLHWyaf0WGsHol6ntrGpqofq8jK11DLNw0P1GIPHgy0eZ+Dzn8caj2NNxLHOzGC8II9JfxfreF+IRov6fklWEQpBNLtiika/DcuwG8sLg5iHZZIw2PSX1oNCZ2JrWlENx1sbpDc3KGTT6jGOAS+hsQmeee3zat+Df3C478klIQSFbJXMblFrjLttrFUe5R1UlIN/yIX1CY5FCyFoHh6qJaWOcqhtbICy0wOzGevkJI5nn8Uan8GWSGCNxzFFIo/GlFtJkt5F/TX33gQIIcSV93pgSZJGgF8GosgbBL4ihPi5m475OPBvgQ3lr35dCPH3zn32Oh44RFuZw7RVoL5boL5TkGOuSrnA4DZjGXbjeCqMZdiFediN8REerva4oVGt9vQ9HG+tk9neolGtACAZDPgHhxlKzhEak5NLofFJnF5f/8+13tLKSruaOd2oarHWgZC9J9b6uM5bepBoFYtdJSVFPSyv0M5r8WVTLIYtHsf18suaehgfR7I8/LLce1H7n7nPx24C/4MQ4juSJLmBb0uS9DtCiIWbjvsDIcT9PpeOe0S72qS+U6C+lae2XaC+XUBU5ZKBZDNhGXHhTg7LJaYRN0bPk51EeVAQQlA8yfb4DumtDXKH++q+B4vdQXh8kksf/6RMEOOTBIZHMfX5g0P1HhRy6CiI02MtEm22GQkOuUg8H5WTS8MuAoOuJzrWKppN6pubt6iHxt6eeozB6cSaSOB57TNY43FZPczMYPTcX/NjpVlh7XSN5dwyK7kVlnPL9/vPUXFH0hBCbAFIkvRjwNeEEHt3OvYO9z8ADpSfC5IkLQJDwM2koaOPaOXr1DZOqa2fUd/KyypCIPsQYQeOK0Esox4sY25MQbtOEA8ArWaD7G5nrIbmQXRHWwciUUKjEyRfepnw+CShsQk8oXDf//87yaXMbkFTD7u93oMnaCMw5GLmWpjgsJvA8JPdFCeEoHmc7k0tLa9QX11FdEpLRiOWiXHsV6/i/cIXFIKIYxocvK/fcVu02S3s9pDDyukK2/lthMLodpOdae/0A/iXyjhPEdED/EdJkk6AXwW+LoQ4upsnkSRpHHga+NZtbn5RkqS3gX3gbwghbtzm/l8GvgwwOjp6N0/9xKOVr1NdO6W+fkZt40z2IgDJYsQy5sZzSSGJUbfuQzwA1Mol0psbHG+ucaxcd4/0NpktBEfHmHnuRUIKOYRGJ7A6HH09TyEE5Xy9hxgyu8We5JLJYiAw5GLqQ2E5uTTsIjjkwvIEew/tUona6qpqSHfUQ+tUm6tlCoexJhI4P/witngcayKBZXISw30qxNPqqUoKHZJYPV2l0lTe00iMekaJ++J8duKzxH1x4r44Q+4hDJKBX+FX7uv5O5CEuJ1tcZsDJekK8EXgdWBXCPHJc97PBfxn4KeFEL9+020eoC2EKEqS9Brwc0KImfd6vGvXrok333zzXOf8JEI0WtQ28lRXctRWcjQOy4BcarJOeLBODGCdGMA86NKnud4HOuWl4811jjfXVKI4O9a+TzkGvLJqGJeTS6GxSXyx/o/VaDXb5A7LZBX10CkvVQraQEeXz6qWlYLDboLDLjwhO4YnVT20WtS3tm/xHRrb2+oxksOBdWYaW1w2pOXLDCbf/flL9VadjbONHvWwnFsmXdGCDz6rj7gvzoxvRr2e8k5hN9nv+LiSJH1bCHHtvk6Ou0tPHQOHQBYIn+cOkiSZgX8N/MubCQNACJHv+vn/lSTpf5MkKSiEyNzFeT3xaJ7WqC5mqSyeUFs/lXdDGCWs4x48nx6Xo68x5xNbPrhftNstcvt7CkHIl/Tmes/cJW80RmRyhsuvfq9KFE6vr+/lpUqhrpJChyByByXarZvGeV8OElSM6cDwo70p7qLRzOVk1ZBakr2HVIra6iqisy7WYMAyNoZtbo6BP/t5VT2Yh4buq7dFCMFh6VBTDyfy9ebZJk0hK1Ozwcy0d5oXB1+UycE7Q9wfJ2ALPLTS8fuShiRJP4qsMELA14EfuY2Zfbv7ScBXgUUhxM/e4ZgocCSEEJIkPQcYkElJx/ugcVSi/E6G6mKWxr7c0GMK2nE9H8MW92GZGMBgeXJNyHtFo1YlvbVJemud4411Nb3UrMsfIEaTicDIGFPXXiA8PqGqCIu9v+WlzsylzF6hp7xUPrupa3rYxdi8X5255Is4nti+B9FoUN/cpLqUktVDKkVtKUXz+Fg9xhgIYEvE8X3/92vqYXoKg+3+1sUW60VWTlc03yEn/1xoaL7WkGuIGe8Mr4y8opaWRj2jmAyPVjnwPGczBvw1IcR37/KxXwJ+CHhXkqTOff8WMAoghPhnwBvAj0qS1AQqwJfEeetlTyCaJ1XKb6epvH0sl50ksIx5GPjMBLY5P+ZQfz+4HneU82ccb6yp6aXjjTVyB/vqaA2r00l4bJIrn/w04fFJwuOT+IdG+r4xrlZpkt0tkN7R/IeTgxKthjJzySjhizrVkRpB5fIkd003T06oLWnKoZpK9RrTZjPWqSmcL76ANZ7AmkxgSyQwBYP397ztJtv5bbWktJJbYeV0hb2iliNym93M+GZ4bfI1lRymvdO4LP1vurwXnNvT6LmTJG0LIR6KI/2keRrtapPyW8eU3zqmvi1/K7GMeXBcDWG/HNTnNJ0DQgjOjg45VtSDrCLWKOZO1GPcwZCSWpokPDFJeGyy7+mlTrQ1s6N4DztFMrsF8hltmKPNZe7yHuSLL+rE+ISOg5c7pjdUYqgtpagup2iltQq3MRTElkhiTcSxJZMySUzcX8+DEIJsNauWlDoEsXa6Rr0tqz2jZGRiYEItKXXKS1FntH+vq3YbzrbhaAFp9rN99zS6oRfHLxiNdJnSHx9QevMIUW9hjjnxfHocx5UQJv/9SeUPMjr+w9HGGscbq8r1OvWKEghQmuNGLl0lPDZBeGKK0NhE35cCtVptLdqqkENmpyvaqjTGhUY9zL40SHDYRWjEjeMJnvbbzGTk0lIqRTW1JPsQ6+tqx7RkNmOZmcb10kewJhLYkkrHdCBwX89baVZYP13vUQ/LuWVytZx6TNgeZsY3wwuzL6jm9MTABBZjH7/UlU/geAGObsiX4wU4XoR68YE+zb2Shl5CuiDUtvPk/9M2teUcGCUcV0K4PjyIZcT9sE/tkUOn/+FoY5XjjTWONtZIb23QVAxMk9lCcGyc2Y+8THh8Sm6OGx3DbLH29Tzl8lKxiyCKZPeLtJvaUL7AoJOpZ8KyehhxExhyYnlCI9CdUd7VVKrHoG5lNbvTFIlgTcRxfeyjWBNJbIk4lvFxJPO9G/pt0WavsCeTw6nmO2zlt27peXh19FUtueSdwWvz3ve/+9xo1iCdUgjiOhwtyD8XDrRj7D4Iz8NTPwDhOYjMw089/0Ce/r3GiPz1O90EPB7Ft8cIrXyNs9/cpPzWMQaXGc8nR3E+H9PLTwoa9RqZrc0eBZHd0YbzmW12wuOTXHn1ewlPTBGZmMI/NNLXeKtaXtotdpWYbi0vhUZcXH1lhOCIHG/1Rp7MoXxaU5yiHhQVUdvYAOX3KlksWGdmcL38sqIcElgT8fuOtZ5WT3vKSh3v4XY9D69NvKbGWofdwxikPv2uukpLsnK4If+cXQWhjGoxWiCUgImXITInE0VkHtxRuCBF+l5fZd7rq+3PvcdtOu4Coi0o/tEe+d/ZRrTauD8+gvuVEQxP8PiFWrlMenNdJojNNY431sju7aib42wuN+GJKZ557fOEJ6YIj0/hi8b6Otq71Wpzelgms1Mg3eU/1Epa5/RAWC8vddCu1aitrt4SbW3ltBKPOm/p1VexJZSmuLExpPsIHjRaDdbP1rWy0ukyKycrHFe0xJTX6iXui/P6zOsqOUwOTOIw9zFYcp7SkndMJoTZz8kEEbkE/ikw9leRvtcYkZ/q54k8iWid1Tj5Wora2hm2pB/v5yYxBe7cnPNBRKWQ53hjXS0xHW/KCaYOnD4/4fFJpp99QVEQ07iDob5+8J67vPS0Xl4SQtA8OupRDtXlFPWNTXURkGSzYZ2Zwf3JT6jKwZZIYBwYuK/nPSofqb5DhyRu7nmY8k7xwuALsjmtEETQHuzf6+meSkuXIJwE692VqHOlOkuHBZYO86QOC+9/h3PiPH0avwT890KIU+XPPuAfCyH+8gM7iycQ1ZUcJ7+yhGi08b0+g+Naf8cbPwzUyiWO1lc5XFvhaH2Vo/WVng5qTyhMeHyKuY++SnhSVhAun7+v51jO10lvF0jvFGQVsa2Xl+6EdrVKbWW1tykulaJ1pi18Mg8OYk0mcX/qU/IwvkQCy+go0n2UDcuNMiunK6ROUnfseRh0DhL3xdWehxnfDKOeUcyGPjUxCgFnu4pyuK4piAsoLdWaLVaPiywdFEgdFWSiOMhzXNA2ZPoe4LKz943cSpL0lhDi6ff7u37hcY/cCiEofmOXs9/axBR2EPjB2Q9kf0W9WpHN6S6SyB1oWfWBcITI5AyRyWkik9OExyf7mmBS9z7sFEnvyCSR3i70NMd5gjZCI26CI26CI09ueUkIQfPg4JamuPrWllx3ByS7XdnxkFSVgzUev69prUIIDkoHpE5SpHIyQaROUuwUdlRj2mV23TJOY9o7jdvSx+BIrSiXkrrJ4egG1DTyxDuqKIa5ey4tCSHYzVVYOiyQOswrKqLARqZES5kXZjEZmAm7SETdJKNuklEPyaibkNuKwWDoW+TWIEmSTwiRA5AkyX/O++m4Ce16i9zXl6m8k8F+OYjvjfgHwrto1GukNzc4Wl9RCSK7t6OO+HYFgkQnp5n72KtEJ6eJTM30lSDabcHpUZn0tqIedmSDuhNvlSTwxeTmuA45BEdcWJ/AVbQd9VBdWpR7HpRoa7ugfYs3Dw9jTSbwfOYzarTVPDJyX55SZ5R3hyBSJ6ke9SAhMeIeIeFP8Lmpz5HwJUj4E8Scsf72POQ2uohBIYnchnaMxS2rhctvyNeRSxCeBdvdvd7PKg1SSmlJJgn5UqxpntmI304i4uHT81GSMZkkxgNOTBeses/z4f+PgW9KkvR15KjtXwB++kLP6gOIdrlB5v+8QX2nwMBnJnB9bOix/MbaajbIbG9xuLbM4ZpcYsrsbKkmtWPAS3RqhvgLHyE6JSuJfi4IajXanByUVOXQSTE16/L5GU0GAkNOpj4UVskhMOTC/ASOXGlms1QXl6gtLVJdSlFdWuzxHgwOh7zr4bOvKaWlJNb4/a0R7fYeugliu7BNW+nEd5gccmpJ6ZhO+BPMeGf6a0xXTruM6Y6CWIBGZwe3BIFpiF2Fp/6iQhDzsqK4i/d1vdlmPSOXlroVxMGZVhIdsJtJRN38+WeGSEY9JKJuElE3rvdYn3zaaLJYqrJYrLBUqrJYrN7x2LvF+5KGEOKXJUl6E3gVOW77588ze0qHhla+Rvqr12lmKgR+cBb7/P2NKugXhBCcHh1wsJLiYGWJg5VlMtsbaszV5nITnZph8pnniExNE52cweXv3yC1elU2qNNKiSmzU+BkXxvOZ7YZCQ67mPvIoFpm8sUcGJ8w/0Ge2LpFdVFRD0tLVJcWe7qmTbEYtkRC9h6Ssw9EPdRaNVZPV1k+kY3pTonprKtsM+QaIuFL8JmJz5DwJYj74wy5hvoXa2014WTt1tLS2Y52jM0L0cvwzA9p5BCaBcv5SUwIwcFZtUc5LB0UWEsXaSqlJbNRYirk4vkJP4moR1UPUY/tju+pWrvNarnGYrHSQxL7NW2C8YDJyKzzwTUE39MYkYeJx83TaGYrpL96nXaxQeAvzWGb7mMT0F2iVi5zuLasksT+SoqqMsnVbLMTnZpR1MMM0alpPKH+mffVUkNTD9tyial7c5zNZSY06iY0IqeXQiNuBkL2J26yb6tYkpcALWkEUVteRlSVb5rKzCVbIoF1NoktOXvffQ9CCNKVtGpMp3Iplk+W2cxv0lJMX7vJro7T6JSWZrwz/Z23VOfLX+gAACAASURBVMrcRA7X4XgJWp1ptiYIxjViiFxSjOnYXamHQrXB8lGBxQOtrLR0mCdf1UpLQ167qhg63sNkyIn5Dl9ohBDs1hoyORSrLJZkklgrV2l2tidKEjMOK3MuO0mnjVmXnVmnjZjVjCRJD2U0uo67RDNXJf2VdxCNNqEfufxIdXWLdpuT/V32l5cUFZEis7ut+hD+oRGmPvQcgzNJYjMJAiOjGAz9KeGoBLFV4HirQHo735NgcvmthEbczDwbUYnC6bU+luW+e0Un2iqrhyW1vNTY0vY9GAYGsCWT+L74RazJJLbZJNbJyfuauVRv1Vk/W7+FILpHasScMRK+BJ8Y+4RKEMOuYYx9ev3QrENm+dbkUvFQO8YZlgnh+S9r5BCMg+n80wJabcFmtqSUlvIySRzl2TmpqMe4rSYSUTefuzpIMiab0vGImwH7nf2y25WWlkoVCq22esywzcyc086ngwPMOm0kXTam7DbMBol2u06pvE6p+CcUd1O8XVqiWOzDulcd94dWsU7mq9dp11qEvnwFy+DDbaJv1KocrKTYWbiukkRnHpPV6SQ2k2Tm+ZcYnEkQnUlgc/bnfLsJIr1d4Hi7QD7d9aYL2AiPuuUS06ib8KgHm+vJMqg7Q/mqi4vUFpfk9NLiYm+0dXQUWzLJwOc/L5eXZpOYovc3GC9TybB8opWVUrkUG6cbat+D1Whl2jvNK6NyrDXhSzDjm2HAeu/9FncFIaBweCs5ZFLQVr7VGy0QSsLUq10KYh5c51oJpOKkVJdLSweaOb18VKCqTBo2GiQmgk6uDnv50rOjJCJukjE3Q947r0yuK6WlhXOUlt6I+plV1EPSacNtMiKEoFY7oFj8LsV0ilRpiWIxRbm8jhCdkIcJs3kMIaaAP7r7/+PbQCeNC0C72iTzv1+ndVYj+FcuPRTCqFcr7C8tsLN4nd2F6xyurdBuNZEkA8HRMZIvfYzYTJLBeBJfdLAv3dS1ckMlhvTWexDES7EnliBaZ2dytFU1p5eora5qQ/msVqzxOO7v+R55nPfsrBxtvQ9zutFusHG2oaqHjkmdrWqznsKOMAlfgpeHX5a9h37vemhUlFjrTcmlijapGM+wTAjx79XKS4EpMJ7/NdRtTC92kcRRXut5CDgtzMY8/ODzY6p6mA67sJlvr6TuprT0otelkkN3aanZLFAspigWl9k7lMmhVErRbHal2sxRJGkYIT7F2ZmLo0Mzx8cSQjzY9/YdPQ1Jkgpogwk7VCmUn4UQor9jQRU86p6GaLZJf/U69a08gR+ew57oT3NarVxib2mBnYV32V28ztH6KqLdRjIYiE7OMDx3ieHZSwwl57A6nH04ny6CUEjirJsg/DZCY27CY265xDTqxu56cuZsiXabxu6uTApd5aXmvtYZ3BnpbZtNykP5ZpP3PVYjV82piaUOOaydrdFs926K66SWOgTRt4F8Qsgm9G2b4pTyjNkhx1hV3+GS3PtgP78vI4TguFBj8SCvNsMtHcrGdEMJUliMBqbDLpIxN7OqMe0h5L5zCavQbKmmdLeCuLm0NOu0M6cQQ29pqUG5vEGxlJKJoZiiWEpRrWo9TkajC5NpjGYzSrE4QCZtZX8f6nX5dSFJEoFAgEgkQjgcVq8DgcDFehpCiEenAP+YQAhB7t+sUt84w/+lxIUShmi3Od5cZ/Pt77Dx3TfZX15CtNsYjCai03Ge+/wbDM9eYjAxi8V2saNJmvUWmd0iRxt5jjbzHG/mb0sQyQ/HVJJ4kgiiXatRW16RzelOeWlpiXZJiW8aDFgmJ3A8/Qy2H1AIIpnAFArd83M220228ltarDWXumXmUtAeJOFL8OGhD6vkMD4w3r+u6VrhDk1x2hpdfOMyKcz/OY0kfONwF/5Ipd5i5bhwi3rIlbUyUGzARjLq5pVkmGTUzWzMw0TwzsZ0sy3YqNRYKGnqYaFYZafa1RxqMjDntPN61M/c7UpL9SNKxXcoZlIsK+RQKq0hhPwYcmlpBCHGaTaf4TTnZP/AwNmpgc73eJfLRSQS4do1jSCCwSCGcpv6YYnmYYnG22Uah5vn/v96P5zrK4skSR8BZoQQ/4ckSUHALYTYeL/7PWkofeuA8ptHuF8ZwfHU3dVMz4N6tcLGW99m/Tt/yubb36F8dgpAeGKK5z7/BqOXniIWT1zo6O92W5A7LHG8medos8DxZp7sbpG2Eht0+ayExzwyQYy6CY09WQTRKhQU72GR6sKi/PPamtb74HRiVbwHOb2UxDozc1/rREuNEsu5ZRazi6RyKZZOlljNrarLgEwGE5MDkzwfe56EP6FuiwvY72/PxLmhNsXdlFzKbWrHWD0yKVz5C71NcXcxb6nTMd1RD6lDmSQ2MyWUlyd2s5FE1M2nL0XVnodk1I3XcefXaKbeZLFYYUEhhsVSheVSlaryoEYJpuw2PuRx8EODAbW8NKSWlkqUSssUiyn2j2RTulhM0Wyeqs9hNocxSCMgXqWQd3N0ZObwEIQwKrebCYfDTE7IxNBRD3aTlcZhmcZhicZWica3jjk+3ERUtKSW0WPBFH1w1YXzjBH5SeAakBBCxCVJGgT+byHESw/sLO4Cj2p5qrZxRvqfv4ttxkvgh+cfWNSzUsiz9u0/ZeVPv8nWO2/RajSwudyMX31GvVxU85wQgtJpjaPNPEcbsoI43irQqMkfgBabkfC4h8i4R712evu7q+JhoplOU+0ih+rCAo0dLd9vDAWxzc5im5vDNjuHbTaJeXj4nv2jTrR16WSJ1EmKxZNFtTGuA6/VS8KfIOlLqvHWyYFJzHdR178vVHLaKO8OSRwvQEMOXSAZ5PEZ3ZHWe2iKK1QbCilopaWbO6bHAg41zjqrlJZG/Q4Md3hv1tptVkpVFjqlJYUgjuvaY4YsJuacdmZdNuZcduacNqYdNmxGA+12k0plSyktKb5DcZlKtSvRZnBgNo/TakUpFQfIZu3s7UtUK9prwu/39xBDJBLBN+Cjla1oBKFcWjnNa5GsRswRB+aoE3PMiSlsp2oqk0nvktne5MXXv9S3yO2fA54GvgMghNiXJEkvXXWheVYj+y8XMflt+L+UvG/CaNSqrL35LRb/8PfZfPs7tFst3IEQVz/5Gaafe5GhxNyF7ImolRscbxXUEtPRZl6dxWQwSgSHXSRfiBKekAnCG3Y8EX0QQggaOzsaOSwuUF3sbY4zj45im5vD+/rr2OZmsc3O3ld5qdVusVXYYim7xFJOJomlkyVOqprxO+waJulP8n1T30fSnyThTxBx9Kl3pqMeDt+Bw+tw+K5MEPld7Ri7TyaGZ364qykueVdNcbeLtS4d5tnNdZU/bSZmox61YzoZc5OIuHHeoWNaCMFex5hWCGKhWGWtUkWxM7AaJBIOG6/4Pcy5bMw57SRdNkIWM0II6vUMxdICxdwS6zud0tIK7XanPGXAYhkFhmm3rpI7dXJ4YOTkRKJTWnI4HEQiEa5e0dRDMBjEVEMjh3dLNH5ni/30IqprbgBT0IFlxI352SjmqJOWR5A722dvZ4vM9hbptzbJbG/RqFZu/uffN85DGnUhhJAkSQBIknTxLupjBNEW5H4thai3CfzILAb7vZmUQgh2F69z4/f/E8vf+iaNagVXIMgzr32e5Ic/Rnhi6oF+GAghOEtXOFw742DtjMP1M072S+rt3oiDkaRfVRDBYRdG8we/k1o0m9TW1qkuLmglpqUlbfaS0Yh1agrXh1+SyWFuDmsyidF979+jKs0KK7kVlk6WVBWxnFum2pJ7U0wGEzPeGT42/DGS/iRJf5K4L96/oXz1sqwWbiaIzkgNySj3OIy92GVM3/201pNSnaWDvKoeUkeyeqg1tVjrZNDJ06M+vv+5UWZjbhJRD4MDd+6YLjZbcq9Dp7SklJnyTc2YHrFZmHXaeC00ICsIp50JuxWTQaLVqlAqrVAsLpHLpNhRDOpGQyNvszmIwTAK4hWKBQ/ptJX9fUG7Lb9fjEYjoVCIkZFe78FhttM8lsmhuVum8WaW7OE27bKmbAweC+aoE9eMD3PUgSFoJV/Pkj3YJr31NplvbZHZ3qR4oiXdbE4XwbFx5l/+BKHRcdzBISRDgL/xtaFz/y7eC+f5hPuaJEm/CHglSfoR4C8D//yBPPsHAMU/2qO2fobv9RnMkbvn02qpyMI3fo+3f+c3OdnbwWJ3kHjxo8x99OMMz156YFHYVqNNeqfAwapMEAdrp1QKshFosZuITg4wcy1MZGKA8Jj7iRjW165U5O7phQXNf1heRtQVI9Jmw5qI4/kzn5XLTLNzWOMzGKz3XoI7qZ6o6qFDElv5LXXuktviJulP8kb8DZUg+lZeEgKKRzIpdBPEyZqWXLJ65JEaT/+gfB29JI/UMJ/fk2m02qynSywe5OXLbUZ5d2KtP/TC+WKtLSHYrNRUz2GxKCuIrS5j2mU0MOey82fDPrW0lHTZ8SjGdLW6S7H4JsXjJRaLKYqlJcrlTTohUoPBjtk8BuIq9bqXk6yd/X0DpZJGWF6vl0gkwksvaerB7/PTztU09fDNEsWjJc6yWsOqZDFijjqwXwpijjgwRZ1UzRWy6W12thdIr2yS+d1Ncgd7tBV/zGgy4R8aYWT+CqHRcXyDo5itYcoFMyf7JbJ7Rbb/Y4lyPg2kz/37eT+ca4yIJEmfAr4HWVf9thDid85xnxHgl4Eo0Aa+IoT4uZuOkZC3AL4GlIH/Sgjxnfd63EfJ02gcljj6+bewzfgI/KW5u1ICucN9/su//TqLf/ifadZrRKfjXP3UayQ+/NEHYmRXSw0OVk8VgjjjeLNAS/l25QnZiU0NEJ0cIDY1gD/m/MCXmVpnZ73+w+IC9fUNdbS3YWBAIYZZtbxkmZi4570PbdFmt7CrEkNHQXSnl2LOGAl/gln/rOxD+JMMOgf7U15qNSG7citBlLWSmzzO+7JCDgpBeMfuSj2cVRosHuRZ2O8QRJ7lwyJ1JYJ6L7HW00aThWJVMaZlBZEqVagoxrQBmHJY1V6HTrR1xGbReh4UY1r2HmT/odXStuRZLMNIDFOtBjk9c3F0aCKdhk5pyWq1qqTQ8R7C4TDmllEmhgPNd2gelRFKEyASmIJ22XdQLu0ByOX3yexsk97eILO9RWZnS22+BXnXTHB0nNDoOIHhMRwDMZoNN7nDKtk9mSBOjyuIjjlvMuCLOQgMuQgMORmw1Jj6eOKBeBrnMcJ/DNn43n3PA2+9XwyICSG+o3gg3wb+bPewQ0mSXgP+W2TSeB74OSHEe24/f1RIQzTbHP/Cd2nl60R+7BmM50wI5Q73+davf42FP/g9jEYTsx/9OFc/9RqRyen7Op9aucH+yil7qVP2VnJkdosgZC8iNOqWSUIhCufAB9usbp6cUL1xg+qNBfl6YYHGnpZzN0UiKjlYZ2exz81hGrz3D+vOYL6O79AhiHJTftMbJSOT3kmSvmQPSfStc7p6JpeTugnieFGbuWS0KH0PXQQRmQf7+Xsz2m3BTq6sksPCQYHFgzx7p1pNPeC0MDfoYTYmG9NzsYH3nLfUEoL1co0bivdwo1hhsVhhr6tj2m82Mue0M++SPYc5l524w4bdaECIFpXKNgWVGGRyqFa7wgpGFybTOM1GlEJxgEzaxv4+NBryORkMBoLBoFpS6lzcDhfNdEUhhrJKFO2CpmwMThPmmEshBwfGkJV8M0d2f4v0jlxWSm9vUsxqRG11OgmOjKsE4QkPYzAEOMu0ye4XOdkrkt0rqWEUkPe++AddBIddeL0S7toRlqM1Gisr8mKslRXapRJzqaW+kcZPIo9DPwF+Ffi6EOLoPe90+8f5t8DPd6sUpez1+0KIX1H+nAI+LoQ4uMPDPDKkcfbbmxT+vx0CPzSHff79o4uNeo1vfu1f8u3/8G8wGk1c+dRnePb7Xr/nzXStRpv91VO2b2TZWz4lvVMAIa8ejU4OMBT3MhT3Eh7zYPoAj/1uZrMKQdygohBF80B7+ZjHZINaTTDNzWLy33v/zFntrCe5tJRb6hmt4TA5VFO6cz3tncZq7ANRCwGn23Jq6fBd7XK6pR3jCCikcAmiV+SfgzN31TVdqbdUU1omiDxLB3lKdSVWLMFkyNVFDh7mYrJ6uBMx36webhQrpLpirSYJph1aYmnOJRNF2GJCkiQajdMeYigWlyiWlmm3OyUgAxbLCIghKpUAudv0PLjd7lvUQzAYhGJLSywpCqKZrqDmeI2SllqKOjFFHdSsVU4yu6S3N8koBHGyv6uWlgxGE4GhYYKjMkH4h0Yx2yJUihaltFTiZL9IsSsdZXWYZOUw6MQftePmFOfpFu31Zbn3Z3mF5qE2X8swMIBtZgZrPI41Hsf//Q8mPXXuKbeSJF0Bvgi8DuwKIT557ieRpHHgG8AlIUS+6+9/A/gZIcQfKn/+XeB/FEK8edP9vwx8GWB0dPRDW1tbPEw0jkoc/dxbOJ4O4/9C/H2PP1hJ8Zu/8LPkDva4/Inv5cNf+Iv3RBb5bIXtGydsXc+ym8rRrLUwmCSiEwMMJXwMxb1EJjyY7lD3fdzRTKcVYrghl5lu3Oh5k1jGxrDNz2uXudn72hyXrWRZPFlkMbvI4skiC9kF9oqaYgnbwyo5dC7D7uH+jPVu1rTGOJUgrndti5PkERo3E8RdmNNCCI7yNZUYFhQPorvvwWU1MRuTm+HmYrKKiEfc2O/wReW86mHeZVcIws68y8aM04bVYFA6pte7iEEmiVpNex2YTF6MxnEajQiFvIfjtIWDfUGrZVRuN6nKIRqNqgRhM1ppHPWWlhoHZUTXdFqj16pGWs1RJ8IrkSsdkdnVlEN2Z4taWQuVuIMhQgo5BEfGcAwM0mp5ektLh2W118lglPBFnQSGnPgHnXjtdZylPYw7q9SXU9SWl6ltbICyogCzGevkJNZ4HFtCJgjj9CT79horpyvyStzTFX7+Ez/f9ym3x8AhkAXO3bkmSZIL+NfAX+smjM7Nt7nLLSwmhPgK8BWQlcZ5n/siIITg9N+vI1mMDHxm/H2Pfeu3/j3/+V98FafPzxs//r8wduWpcz9Xuy04WDll83qW7RtZNd3kDthIvhBlbD7AUMKH+QOw/e9mNI6Pe0tMN27QPFb8AEnCMj6O49o1hSBkJXGv85c6i4E65LCYXWThZIHjsuY/jLpHmQ/M80b8DWb9syT9yf41x5UySmKpiyAyy9pQPrND2Rb3ukYQkTmwnD+YUW+2WUsXNf9BURInJa3cMuyzMxvz8Lkrg8zGPMwPehj23XkgX67RVEdp3CjKCuJ26uEFZd5Shyg66qFWz1AsyrHW1Z3OvKXVro5pMxbLKKI9Q7P5AidZO3v7BooFLdaqGdOagvB5fYoxrZSWUiXODm9wctJlTFuNmKNOHFeDmKNOjGE7JemM7NEO6a0U6bc3yPz7TfJp7TVidTiVuW4vExwdxxsdQTIGKWTbZPeKpPeKLP1piXpFq/S7/FYCQy7GLwfxBU24a2lsx2s0VlNUf3eZ2vIy9UKBzm/BNBjDNhPH9corsoKYmeEs6mK1uCHvSj9dYTn326z/7rra3GmUjIx5xs79Wng/nKc89aPICiMEfB34tfMuYZIkyQz8BrJ5/rO3uf2xK09VrmfI/l+LeD83ieulO0fY6pUyv/2L/5TlP/4Dpq49z6d/9MewneNDrd0WHKyesvrmMWtvHVMpNDAYJQZnvIxdCjB2KYA34vjAjAEXQtDsEMR12X+o3rhBM62kPSQJy+SkXF6an8M+P491dg6j696S30IIdgu7LJwssHSypBJFp//BIBmY8EwwG5hl1j/LbEAmiL7EW9stOFF6H7oJotD1dnDHunwHhSD8E3c1ViNXqqvqoVNiWjkuaDOXTAYSEbeiHGQVkYx57jjO+3bqYaFY6ZnWGjCbmHfJndLzSolJUw81SqXVntJSobhEo6HFSM3mEAbDKI16mLO8m+MjC4eHWqzVbDb3lJY6l7s2pmNOmq42ubM90ttbijG9SXZnm2ZDISuDAf/gcI8xbXFEqZatnOyVyO6XyO4WKXSRkNlmJDjkwj/kIhC14zEV5dLSxjK11DK1VKrHdzO4XDIpJOLYlPJSe3yY9fYRKzlNPazkVjitaZ3lYXuYGd+MtjPdM8FEo4k1u4p05Qt98zR+BvhVIcR37+qB5U+1XwJOhBB/7Q7HfBb4q2hG+D8RQjz3Xo/7MElDtNoc/q9vIlmMRP67Z5CMt//gPjs+4td/5u+S29/jI9//l3j2c3/+faOz2b0ii988YOW/HFHO1zFZDIxfDjL1TJjReT8W2wdjIHEzm6Xy7rtU371O5fq7VG8s0MooRqAyg8neXWJKJjE4740gWu0WW/ktFk4WVHJYyi6pe6dNkolp37RKDrP+WeK+eH/WitZLcud0N0Ec3ejqnDZCKHETQVwG5/m3PraVxrhu72HxIN+zSjTosirmtOY9TATvvGc632yxUKxwXfEdbqceZjreg0IO8y47IUU91OsZxZhepFhYpFBc7BnlbTBYsZjHabUHKZd8ZE/s7O9JPbFWn8/XQwzRaBSve6DLmFYUxC3GtFktK5mjTowhC/lmjsz+FumtDbW8VMppPRiOAS+hsQmVIFy+QdrCS+6orhBEkZODEm2l8U4ySHgjDoJDTvxDLrzuNu7yAcbdFa20tLqqxroxGrFMjCvEkMAaj2OemWbf3VBJoUMSu0VNoXSWWqkE4Z1hxuTGe7qrjWo5XoB0CtrKhOSfyvfP07hp9lQIcL3f7CnlPn8AvIscuQX4W8AogBDinynE8vPAp5Ejt//1zX7GzXiYpFFbPyX9lXfx/8Ukjsu37/Y93lzn1//BT9Js1Pm+v/7jjF66cufHKzdY+S9HLH7zgOOtAgajxPiVIDPXIoxdCjz2ZadWsSQriHffofLudarvvktjf1++UZKwTk9hm7+klZiSSQyOe/vAbrQbrJ+us5BdUEtMqVyKSlNO71gMFjW5NBuQLzPeGSzGPszFquTg4B2ZIA7eln/OrnT1PgzIcdZugggl76r3oVRrsnTYSw6pwwJlxZw2GiSmQk7FnNb8hztFWztd0zeKFa4XZIK4Xqyw3dX30FEPHYKYd9mZdlgV9dCkUtmkUFhQFIRMEPW61i9gNocxGEap1yKc5d0cHZo5PGwjh2bBYrH0EEMkEiEUCmFuGGTlcFCicVCkfvD+xnTdXleN6Q5BdBvTRpOJwPAYoTHZe/DFRjGYQ1TyJjJ7WmqpWtLUk3PAokRaXfjCFtytE+yZDZorKarLsjHdympqyRgKYlOIoaMgCoMDrJS3eshh/WydmpJsM0gGxjxjvQThHGKodIqhMyq+s8u8qikOPENyyTI8p15Lsct9TU/ps6eAs9/apPCNXQZ/4gUMt/nmv5da5Nf/wU9icTh4/X/6KYIjt68jZveKvPP7uyz/ySHNRpvAkIvZl2LEn4s8tsP92vU6taUlWUW88y6V69epr6+rmwDNw8PYLl/CfvkK9suXsM3N3bOCqLVqrORWeghiObdMQ/lG1UkwdZeYJgYmLn56a2cpkEoOb8s/n2qzh3APQuwqxK5o5vRdzF3q7Jq+2XvYzJY6/9XyWA2FGDrkMBO5c2Ncvd1mpVzrIYcbxQpnTfkDVULue5hz2bmkkMOlLu+h2Szcoh5KpWXabfmDT10E1B6iXPaTzTrY25Mol3vnLXWIoXMZcHlk9XDQlVw6KNHu+uA2Dli0WGvMgRQwc1o+JrOrlJa2ZPVQLWp7J9yBkEoOwZFxbO4YzYaL3IFsTGf2iuQzFdVdNVmNBAadBIZc+GMOBqxVnPkd2JSJoZZKUd/aUnt+JJsN6/S0VlpKJBCTo2waTrTSkuI/dI+FCdqDKjnIpaVJJtsCW2a1lxy603AWd9eYePlS8SZYzht79pGnDgt85ye+p2+k8V2U2VNCiKeVv3tHCHHnr9AXiIdJGkf/5DtIFiPh/+bqLbfJhPETOL0+3vjbP40neKsS2V064du/tcXuUg6j2UDiuQiXXh4mOOJ6rDwK0WpRW1vTSkzvvEt1eVldFGQMBrFfuiSTxJUr2C5duucd1I2WLNNvZG9wI3ODG9kbrOZW1Yirx+JhNjDLnH9OJYlRz+jFJ5iEkGcvHbyjkcPB21Dq6rz1T2nkELsqX+6ivFRrtlg9Liq9DwW1Oe60a6T3qN+h9jx0/If3MqdPG01uFHvJYblUo6F8DtgNBuZcckmpQw5Jlw2nsdM1vUOhuEixoKmHalUrmxiNAxiNY9TrEfL5AY4OTRwdGdRprTab7RbfIRwOY6yhqYdDWUE0jrvUg0nCHHF2lZccVM1lMsc7PeSQO9zXvqhYbQRHxwiNThAcHWMgMoLBGCKfFWT3iuqlWVc+7CUYCDsIDMkE4fMZcFWPMO+vUF+WTena8jLtstZ0Zx4dxRqfURWEJT7DkU9iJb/WQw7b+W2EwkJ2k52pgSni/rhMEt5pZixe/Kd7GjEc3ZBLS51eGskIgWmFGOYgPE8rPMdWM0DqqCjvBDmU1eXWSVn9AmE3G4lHXCSibv7RF57qG2n8qRDiOUmSviOEeEaZPfXHTxpptAp1Dn76W3i+dwzPK6M9tx2spPj6T/9tnF4fX/iJv4/b3/vBsL96yp/+u3X2lk9xeq1c/vgQ8x8Zemy20jUOD6l8920qb79N9d13qSwsIJQ3jsHlwnbpkqweLl3GfuXyPa8ZbbabrJ2usZBdUEkilUupCsJj8TAfmGc+OM9cYI65wFx/OqhbTTmtpJKDUmrq7H0wmORykkoOV+QSk+38cd9CtcHiQYEb+2dc38tzY/+M1eMiTeVD02oykIy6u5rj5NEabtvtX0NCCLar9R5yuF7ojbZGLCaVHOZddi655ZlLRkmi1apSKi2r5aVCcZFicamra1rCYhlBiCEq5QDZEyf7ewaKRSMg9SwC6r54nG7Ne+giiXaxSz14LDI5xFyYYw6ERKJ0XwAAIABJREFU10CudCj3O+xskt7aJLOzSb2iNA5KEt5IVCEHOdZqdUWpVRyc7JXJ7hXJ7BUpnnT1PDhNBIfl0lIgasfNGY7cFq1VrbTU3e9jGBhQDemOgqiORVit7arksJxbZvV0VS2JSkhyack3oykI1zDD5QKG9GKv91DWyli4oj3kQGSerH2MpUxDXRiVOupdN2uQYDzgJBF1K+PePUxHXNTtBlKlGovFCj8+PdQ30vgbwAzwKeAfIM+e+ldCiH96v09+L3hYpFF665jcr6UI/9WnsAxrSZrcwR7/6u/8TawOB1/8uz/TQxjFXI1v/GqKjbcz2D0Wrn1mjLmPDD7SfRTtel1ulFNIovLd76q9EJLFIndSX74sk8Tly1jGx+9pPlar3WIzv9mjIJZOltRarsvsYi4wx3xgnrmgfD3sGr54gmhUFIP6bU1FHC9AUzGPTXb5Dd1dYgrP3ZX/kCnWuLGf5/reGQv7MkFsZrVvr0GXhbnBAbm8NKiZ08Y7jHqpttqkynJq6YZSYrrRtS3OgBxtnVcUxCW3XTGnOxNbj1X1UCjKJFEub9CxIuVx3hM0GlGKhQGOj+VNca2WXKLteA/RaLSn7+Hc6qEzyjtip2wokjneJr21oSaXemKtTqdKDqGxcTyhYYTwk8+0yOwVye7KxnRL+TCVDBK+qDZOw+tq4SrtYdxZobackpNL6+uqSsZsxjoxgTWRkBVEIoFxZpIda1nteeiQxFFZ63H2Wr3qnpK4L07cO8Vk24g9u9pLDicbqHWv7g2ECjlU/UlWixalrJRXfKoCmaJGeEGXRd0Fkoi6SURceLw2NuoNFpQ94wvFCqvlGnWhBRT2Xnm6r0b4Xc+euig8LNI4+bUU1eUcsR9/Xp3TVD475Vf+zt+kWi7xA//zP8IXkyO4QghSf3LIH3xthXazzbXPjnPl1RHMj1hnthCC5sGBSg7l736X2sIiQnkDmQcHsT/1lHx5+ilsiQSS5e49l7Zos53flglCIYnFk0X1G5ndZGfWP8t8cF5WEoH5/pSYqmdyaqm7xJROgVBGNFgHZGKIXdVURGAajOdLsnWWAt3YP+PGfl65nPXsmx722Zkf9HBpcID5IQ/zgwOE36NzOlvXyksdFbFS1kZ6O40Gtd+h4z8knfJYjXa7Qam8RrGwKPsPioLondgaRZJGqVWD5HIuDg5MnJxoXdMDAwM9BKEmlzJVmRS6/Ifbqwf5IrwGcsUD0rtycim9tUFmZ4tmTfFBDAZ8sSFCYxNyrHVkDIstQrloVYfxZXeLlM40Y97uNqvqwR+y4G5lsaXXaK4opaVUitbZmXq8KRpViUEuLcUpRN2sFDd6yKF7HW5noVUPQVgCBPMHSKoxfQOOl6DZUUIG8E92kcMcIjzPLmGWjkqkDuWhjanDAhuZEq0udRmPuNVFUcmoh5GQg4wkejYGLharnDa1sSKDVjNJZRFUZ2PgtMOK1Wjsb0f4o4KHQRqiLTj4+9/COu0l8KUkIO+8+Nrf+1tktjb5wk/8fQbj8t83Gy2+8avLLP7RAbHpAV79oVm8kT5EOM+Bdq0mq4i3vqupCKVhTrJaZQ/i6lWZJK5exRy+++2DQggOSge8k3mHhYxcZlrILlBsyGUNq9FK8v9n782jI83v6u7PU/teqlVVpb3V2qXeZnrMjD32gM1mj9mdODEBBxNyEgwhhjcJCTgHQ8yWQMAkAV4IOwSvhM02wXjMeGY8W2/aqqRu7UupqlRS7Xs97x+/Z6lqqae7x+5Ocl5+59SpGbWkqiOp6j73e+/3Xv+kNmaaCcww7BnGeB97Bq/rFFPKWOm67mA66jAAuno7wEEBiPsI52u22qxlSgIgdgVALO3nyVXEG6dBgtGQi9k+LzMxwSBmol68d0gTbssyG5U6C4qtVR0x7XeMl2JWc/d4yWVnyG7BoMRqqCOlYmGJQjF+22KcBYtlmHYrRrHkI5O2sbsrUauJ34PBYCAcDmvMQb23tkzdo6X9Eo10GQ21bmMP5l47ZVNJZw+bwr2UT+tX6TaXW4CDAhCuQD8yPRwnG9po6Wi/RFt5DINJwh916mF81hqu4g7SRlzbeahvbmrahuRw6HEaCoOQRwfZlA+7wGHlaIWj2pH2vMKOcDc4uIcYrlUwp1d0cDhYgpLOhHCGusCB3hny7lESh02tLCqeLLCSLFDoKIwa8NtFF4gCDmO9LtoOEyuVmtL7IcChM7XXaTRoLYGTSrTKpNNGj8lApbKtbMuvUCzGKZUSPPH45x4saEiSVOCU7WzEJYcsy/Lrz2f4Ms7/DtCo7xZJfeQqvneN43ykF7nd5k9/4ae5+cqX+KYP/Chjjz0BQCFb5TO/vkBqI88j3zjEY+88c8eWsIdxWsUilatXKb/8CuVXXqEyP6/RcHN/v84izp/HNjmBZL5/jaVQL7CQWWA+M898ep75zDyHVTGfNRvMTPgmNHCYDkwz2jOKyfCAd06Kadi/BntXYU+5L+zp/+4b7gCHC+K/3b33/O2rjRaJZEFjDot7eeLJvDZftpgMTEXcTMcEQMzEPExGPHeM1ii32sRLKnuoihFTqUJZGS8ZJRh3dIvT0y47AYsJWW5TqWwq4yWVPSzdFqsREOJ0LUw+7yGZFFWiqrXVbrd3MYfe3l6CgSDyUZ3GnrC0NvaKJ9iDwWPBEtXFafxGsqUDRXdYE7lLHUVAkmTAF41pAOHvH8JsFXlL6kLc4W5Ri+wHcPaIjelgvxNf0IKnkcJ6sEZjNSHylhIJ2kU9ndY8OCiYw8QE1olxLBPjpL0Sq7mbXeCwVdjS4ujtJjtne84Kx5Ky8zAu2fAebXWDQ2dEvMkmdKzeWQ0cGsEp1isOXXdQAKIztNFjM2lFUeqIKeC3sdnQK2XjxSorZX335fbU3imlOXDAZqHVPFYWIvW8rVJphVZLHXdK2O2DuFwTnD/3q3/HNB7WyT+zTf4zG0T/3Rswui289D8/zrN/+Nu85R+9j0ef/lYAkms5/vK/3aDZaPO2905z5sLrb217vaeZzVJ+9VUqr7xC+eVXqMbjwgZoMmGfmcH+6CM4Ll3Cfv48puC9u3jU02g3WD1aZT49z43MDeYz86zn9Kv1Yc8w50LnmAvOMRecY9w3/uB7IEoZHRhUoMirm7WSGCfFLghwiJ4XFtf7SG/NVxuK7iAAYmkvz2qqqI0Q3DYT01ExVpqJeZjt8zIauvNyXLre0Kyt6njpVrmmLTK5lfHSjMvOjFsAxLhSJyq6phMUlPFSQbmC1N8gjFitg8hyH+VygOyhQ4nV0J+LKk53goTT4qB5UNaAob5X7N6a7tx7UMTpiqlMJr1FemNd0x9yBzpQWZ1OhTkI/cEd6Kfd9nGcqgtb606R44OyHuVtNui21piTHlsVZ25L2FoTK1QTcRpb2xp7MDidWCcmsE1OYB0X9/XhKLdqu13sYfV4lVJDz4EacA90swdHlP7SMYZO11JqCeq64I9vWLe0hqeRe2dIm2Isp8oaOCwnC9xK6ZHvJoPEaEhEvk9EROz7YMhJ3gTL5Spxpe9juVTlsKEzjrDFpIHClNPOtMvGmMOGRWpQKq1pVbIlBShqdZ2xmc0+XM4JnK4J3K5JnK4JXM4xJMnG8fExgUDg70DjYZ30r9+gXWnS+y8usbO0wEd/8t8y9tgTPP1D/xpJktheyvKXv3oDh9fK099/Dt9XsMT9tU4znab0pRcpv/IK5VdfoX7zFiBGTfYLF3A88giOy49iP3/+vpfmZFlmt7jLQmZBAER6nuXssiZU+21+DRzmQnPMBmfxWB4w+Swdwv7VDgZxrbteNHBWgEPsogCKyLn7cjClClUxVlIAYmE3z1ZWF6hDbqvGHGZjXmZiXgb8p9tbVffSfKHCfLHCjUKZxWJ333S/zayxBlV/GLQJzaheT1EoLHa4l5aoVLZQyb/R6BaR3s0ohYKX1IEqTovnosZqdI6XwuEwpipdzKGxX6J5qO8kSHaTYA8xF+aoEylg5qhywOHuJilVe9ha73Iu+SI6ewj0D2G2RwR72BXsIbNd7FqKc/ttBPrFaMkXMOOup7AeKGF8cbE13S6VtO9vGRwUzGFyAtvEBKbxs+y5mieE6b2SzibdFnc3OHjPclY24Di8pYPDwUL3Do3N29082DtDuWeMlSNZ6A77BYU95DnqsD1HPDahO0SF9jDe68bqsbCqlEKp7GGtUtNGN3aDxITaNa7cTzrtBMxGarX9DuaQ0IwJ6ta8JFlwOs/ico3jck3ick7gck1isYSoVqscHBxwcHBAKpXS7uv1Oj/xEz/xd6DxME671mTvQ1/C9aY+LG/087v/6gew2Oy858O/iNXhYO1ams/+xgK+Xifv/MHzD7SrolUsUX7lZcovvEDp+Reora4CwvZqv3QRx6OXRYjf7AyG+xSsy40yC5kFrqWvcSMtWIS6eGQ1WpnyTzEXmuNc8BxzobkHb3UtZxVwUBnEdch1vMD9owIYYhcVFnFOvOjv4agC9cKuGC0tKCOmdEdz3KDfwawiTE8rQBF2n+6QUrOXVHCYLwgGoS7HmSSYUOI0Zjs0iB6zOl7aolBcUkBCAEVn7pLF0o8kDVCtBDk+drG3ZyKblemM9L59vOTz9tA+rAmA2C/S2BP37VJHYqvfpgGEKeqgbqtzmN0itanuPaxzlNzXru4tdgehoWENILyhAWT8HKcaZHaKZHa6tQejySB2HvpFnHePtYIzt4W8lqC2kqCaWKGxpf9ODW63YmfVAaI0EGC1ut01Wrp1fKsrjG/EO6ItxI37xhm3henNHyCllgQwHCyKRGDVAScZRRy8thA3Szs0zVbTR/ygoIyXCiQOupcm7WZjhyjtZjLqIRawsye3NdagupdKCuOQgGG7RWMPohBKaE9yq9hRBpXQtIdmU19EtNn6FFAQDMLlmsRhH6bdljg8PNQAQgWHfF7PhLXb7V09II8++ujfgcbDOJWlQw5/d4ng987y2T/5L6xffYX3fPgXCQ2NsDGf4dO/Ok9o0M3T7z+PzfmVHcXI7TbVxSWKf/sFSs+/QOX6dWg2kaxWHI88gvOJx3F81ePYpibvu2EuWUpyLXWNq6mrXEtfI5FN0FJcQyPeEeaCOkCM+cYe7DZ1OdutQexf674C9J/pZhDR8/cNEDd2cszv5ljYFfeqQG00SIyFXQow6CK15w77D/V2m5VSlfliRbAIBSAqyjaw1SAx7bQz51ZuLgeTTjFe0t1LAhgKhUUKxWVt90HfnO6nVPKTyYjN6WpVgINaCHQ7QNiNViFO74nRUmO/ROOgBM2Ti3GWmAtj2Eq+dUQmuUl6c43UxjrpjTWqJWUko+49KOAQHBjG6oxQLdvJKhvTme0ipWMdZB0eC8F+F8EBF76gGY/KHhTdoWspTkkp7hwvGcfOsOOssXK8wkpWsIfEUYJMRS8oCtqDGjCM+cYY95zhTLOFJb2ig8PBYrd+5Qjo7CEiGMSRY0TZecgT3y8QPxDCdKXRUp8ewwGnJkpPRNyM9bqo240kStUugOjce+kxGTXmMO0SIDHhtGGXZCqVDT2QUekZ716KdOFSQEEFCZdrAqPRRaFQOAEO6XSatto6aTAQCoU0q7NWFOV2d13YSZL0d6DxMM7Rn9yk/OoBR19d4bO/9p9583d+D5ff+W3sxLP8+a/cwB9z8s0/dOEr1qndKpYoffGLFL/wBYrPPivC/CQJ28wMzscfx/nE49gvXbqvnupmu8nK0QpXU1e5nrrO1fRVkiUxf7ab7MwGZ7kQusDF8EXOhc492Ea5WlGAwu6r4rZ3rTsWwTdyG4M4f88ahAoQ87s5buwIgFjYy2kb1GajxETEzVyfl9k+L7MxLxMR9x3jNSqtNsvFigYQN4pl4sWq5n13Gg3MKXsPcy4H59x2zjpsmA0SrVZFjJUKSxSKAiRKpQRt5QrZYLBhNo3QaEYp5HtIJi3s73dvTneOliKRCMFgEKnU1kdLikjd6khTNThM2mjJHHMheyWOSnuktoQ4ndpc53B7i3ZLsZBarIQGFfYwfAZfbBDJECKXamh7D11b08reQ1AZL/VYKzjz2xg2lKW4eILGjv5maPB4NGHaNinuK/1BVqtbJLIJEkcJjT2oS5xmg5nRntHbbK1+Arld0RmibUzHtTA+DGZFmNbjNGrBKW6VnMQPCprukEjmuyzPfqeFyYiuO0xE3Ph9NtaUnQfVtbRSrlI7pRCqs042YjHRaBx2jZVKxRVK5VXt9y5JRhyOMx3AMInTOYHNFqPRaJBKpbSxknqrVDqEdI+na5O+t7eXYDCIseOiUZZl2sVGd/xKskTkhx55aMt93wb8LKJDQw2q//+Ne2r/519G8hr52PM/TXhklHf9+H8gu1fmkz9/BXfAxrd84OKXnRfVKhQofv7z5D/7V5SefRa5Xsfg8eB605twveXNOJ988r7a5or1ItfT1wWLSF3jRuaGthMRdoS5GL7IxfBFLoQuMO4ff3AsotUQoqIKELtXxAtddaD0DCnsoYNB2O8tbqQTIOZ3c8zvvDZAzPUJgLCaTgeIQrPFgrI1faMoRkyd+w8+k5E5t51ZBRzmlO1pYW/NaeMlYW9dolS6hbocZzR6MBlHqNd7Oc552d8zkU4bUN1LPT09RCIRotGoBhIel5tmutoFEI1kiXZZHy+ZAjYdICIOKtYqh+lNUltCe0htrFHI6LEmTp+f0NAI4aERQkNncPTEaNbdHO6VtfFSPq2/QVkdytZ0v4tA2IK7eYj94CaNm3Fqy/Fu9mAwYBke1piDdXIC09hZdh1VTXdIHCVYya509aQHbAEm/BNM+CYY948z7h5mpF7DnE7ousPBYnc8izvaAQ5zyL3TpCyDLKUqgjkkRWDjWrqkbdR3dpGrDGIk7CJraLNcqoqb0jee6RCmey0mbaQ07dJ3HkxyjVJp9TbtIdG182KxhDXG4HJOihGTcxQwc3x83AUMBwcHZLOd+zLmE8yht7cXu93e/TpotGgc6HWzjYPyyXwujwVTxEn4fQ8vsPAm8E5Zlpe/3Af7SpyHCRrNwwrJn3+FDVucK2uf5bv/43/BZOnh4z/7CrIM3/GvH8Xle30aRrtUIv9X/4vCZz5D8fnnodHA1NuL++u+DvfXvg3HpUtIpnuzppYaJa4cXOHlg5d5ef9llrJLtOU2BsnAhG+C86HzGlBEnK8v4uOuR81i2r2ig8T+dX2O7AhA3yP6LXYJnPdWYnQ7QKgjpk6AGO91c67/3gDisN5kQdEfFhQWsVbRrz57LaYucJhzO+i3CmAVArU6WhIMonPMYDaHkaQhatUQR0dudneNHHdUigaDQaLRKNFoVGMQNski0lr39OTWxkHn7oMBc8SBRRWnQxbyjUPSexvK7sMa6U1dnJYkA/6+fl2cHhjGZOmllDMKYVphD7UOAPKG7BpA+NwtnIVtTFsr1FYEQHTuPRjcbsEeJicFSExOURsIslo5yR5U44S6FDfhm9DZg8lDMLfbPVrKrOrLlSZbRxjfbMfGtFXkcHUARKcw3ddjF8xBtbX2ujC7hTC93FEpu1apaT9im0FiwmnT2gJ1YdpApbLVMVYSI6ZKZRPVPWAw2IUo3ak9OCewWPxUKpUT4JBKpWg09Ofr9/tPxK309PRg6EhakGWZ1nHttlbBEs2OYEXJbMCkudw6IuCVsflDG09JkvTc/65E29POwwSN4gt7HP/PW/zF9q9z+Tvfxdxb38Gn/uMVjg7KfNuPXCI0cH/FPLIsU3n1VY4/8Unyn/0scrmMORbD/fVfj+frvw7buXP3FMlRbpS5lrrGS8mXePngZRYzi7TkFiaDibngHJcjl3m091HOhc7hND8gJ1cxDXsdALH7qogABxG1EbugAMQlcX+Pi3J3AwiTQWcQc/2vDRCyLHNQb3aJ0zcK5a459IDNwpxLB4c5l51eq/k2gXqJYmGRfGHxhEANg5TLQQ4zDnZ2DJTL3ctxKkBEo1ERrVGS9UhvRZxudfRAG5xmzDExWrJEnbTcMoeFXdJbgjmkN9fJ7u0gK/Nsi92uL8YNncETGkCWfRwd1MlsC3A4SurWVpPFoOw9KGVAUg5Hdo32zQTVeJxaPE7rWI/YNg8MKMAwiW1yEvP4GLvuhiZKJ44SJLKJrkgNv83PuG+cCd8EE/4Jxt2DnKlVMafi3c6lzihv72DXaEnuneHA1M/yQUlL8o3v51nr2Ji2mQ1MRDxMRdxaFld/yMleu6XsPFS1xbh8s6091KDNIliD0y62pl02RuxW2s1cd894KUGxuEK7rbIvCbt96IT2YLcP0m7LZDKZLtfSwcHBCWH6dnAIhUJYbjOttKtNjTF0jpfkmr71bfTbbgMHB6aAXUur6DzNep3D3W0iZ84+NND4JSAC/Amg/XXLsvzJL/fBX895mKBx8N+vc7y8wyumv+bdP/XzPPN7K8RfTPKOf3aO4XP3vufQyuc5/tjHOfroH9PY3MLgcOB5x9vxfuu3Yb944a5X/o1Wg6upq3xp/0u8nHyZhcwCTbmJSTIxE5zhschjPBp5lAuhCw+mQKhe7tYhdl/VhWrJILKXVHDoewRCU/cctXGQr3Jt+5jr28caUJwGELN9Xs71vzZA7NcaXC+UuV5QXEzFCmnF4qrGe8+6BDicU7QIn9mk9U4XCguKBiGAolOgtpiHaMv9lIp+0mk7OztQr4vnoY4SOgEiFAghZ2vUd4tCe1BYhNY3rTbGdQTz1aw10ukNUhvrpDZukdpYo3ioC8HuQIjQ8Ajh4TOKOB2lVrFzuFvmcKdIeqdIJa9vDLt8VgL9LoJ9Lnx+CXcliXlvhUZCAYhbt7RlT8lqFR3Tk5PCuTQ5SX0kys36nsYcVrIikK/aEuxRdS6N+8bFiKlnnAlLD4GjXaTUgqI/LMDhTX0kaXZ2gQO9s1T9E6zmjFqK77KyOX18G3vQWgQjHiYiLloOEyvlmqY9LBWrXX0fbqNBEaR17WHSacNpaFMur3eMlZZP9IybzX5lrNSpPZzFYLBTLBZPsIfXI0zLbZnmYUd4Y1KMmTo1Kslm7GoVVAHCYD35+pJlmWL2kPTWutif2drQekPkdpsf+ehfPDTQ+K1TPizLsvw9X+6Dv57zsEBDbrbZ/uDfspabZ/r/eQfpbSvP/EGCR98xzBveeeaevkd9Y4Ps7/0+x5/6FHK5jOPRR/F+x7fj+bqvu+vexE5hh+d2n+OLe1/kxf0XqTQrGCUjM4EZLkcuczlymYvhi195kJBlAQg7L8P2i7D9knjhq33UPYPdY6bo+Xvuos5XG8zv5DSQuLGTI5kXLxCT4fQR051E6lStwbVCWQOJ64WyBhDqBvWc2845hT3MuOy4TEba7RrFYoJ8YUGzuJ4QqM0jtJoxCgUfBwc2dnf1WlGbzaaNllSA8Ht9tNJVGrtF4V7aFQI1ytWtZDaIF3tMAIQpYqdIjvSOYA+pdQEQaueDOl4KD58hPHwGf/8IJksv+UOZzHaB9LYoBWqqCadGCX/MSVCN1TCXcOW3kNfEaKmaSGihkwCmUEhjDtbJCSwT46T8JhL5VU13SBwl2C/pKa891h5dd/CNM+E5w2ijgSWdUMBhXtxX9Lk83kHFsSScS3LvLEljhOVkUYt6jycLrKWLWoahamvtBIiw385Ou9k1WlopVamcsjE9rQrTLjv9VrMiTCc0BnEyTsWM0zmqaQ4u1xQu1wQWS4hGo0E6nT4BEJ3CtNvtPsEeAoEApttGy61S4+61syF7NzhEnRi9p+eQNWpVDre3RKmUomFlNjd0BxzgCfUKi/TgMMHBESafePLv3FMP8hSW9sn97k02A6uMv/tdfPxnX6Fv3MfT7z9/12iQ6vIy6V/5LxT/5m+QTCY873gH/u/+LmxTU3f8mla7xY3MDT63+Tm+sPMFNvIbAPS5+nhT35t4Y+yNXI5cxmW5e8/4fZ1GVWgPOy8pIPEyFJU3GLNTMIiBN0D/ZQESrnvbdK81WyzvF7iuAMT1nWNupfXN3JGgk/P9Xs4P9HCuv4eZmOeOAHGojJg6AULtn5YQ9aLnPXbOux1cdDuYdtmVgL46xdIKhfy8AhLzFIsryLJitzW6MZtGqTci5HIeDpIW9vdlVIHa5XJ16Q/RaBSPwy22p3eLGovo1B8kq1GMlvpcmPuEvfW4klLGS7c4WL9FenNdC+YzmkwEB4cJj4wSHh6lp3cQWQpwnGyQ2REAcZzUdwUsdiFOhwbcBHotuBtpbKmbNBTtobq6qsXWYzRiPXOmCyCksyOsG7PEs3Hi2TiJrGAR5aYSdS8ZGPYMawAx4Ztg3BognNtHUsdKyQXIJPQLCU17mNWaB6uBKVZyBk17UAFCtTqDCGuciurjpbO9bup2A/FSlUUljG+pWOGgYyEyYDYx3bEQN+2yM+awYVU3ptUyqGKCYilOva4zNV2YnsTtmhI7D44RwNQlTKvjpcPDzo5y8wlROhwO47jt4k9utml0Rr8rANHO37l21hx1Yg7bkU75+5dlmUImrezOrCsgscHx/h6ywt603hB1A18BCquj+2LuYWoa/cBHgDciJJcvAv9CluWd1/zCB3QeFmjEP/IZHDs2TN8V5ZmPH1MrN3j3jz/2mk6p2toa6V/+CIXPfAaD14v/Pe/B9w/ejSl0+httvVXnxf0X+dzW53hm+xkOq4eYDCbeEHkDT/Y/yRtjb2TIM/SVFa7ze4I9bL8kgGL/OrSUP2jfMPQ/BgPKLTxzT2OmdltmLVPk2nZOYRDHLO3naShvpEGXlQsDPVwY8HKuv4dz/V56HKf/HHONJjcKlS4Wsd0xchi1WznvcXDeLUBizmXHaTKKHYjSigAHBSSKxYR2RWk0ujEZz1CrRzk+8rK3Z0a8J4ifbU9PT9d4KRKJ4DTb9d0HhUU0U2VNeDQ4TJj7XEKg7nNBwEg2v9c1Xuq0twr94QzhkTOEh0dx+vppNb1k9yqkt4tktgsUO/QloMbsAAAgAElEQVQNZ4+V0ICL4IAbX4+Mu7yPaWuZejxONR6nvrGhtcVp1tapSWwTAiCKfT2slDYEOCjaw0Z+Q8tccpqdmu4w6Z9kwjvKaAtsmVWls1zpLi/qeoVwLs1qDELunWXP1Ef8oEw8WWBpP098P896pqSxB4dFZQ86QAT9drabTZZKatd4lZWSbme2SBJjTqsmTE8r2kPQbKJeT3UxB7Ex3dkzbsHpHBPswT2ljZgslgCVSuWEpVXdmFZPpzCtAoXP5zshTLcL9RO6Q1f0u1HCHHZ0MQdzxInRffrffr1aIbOlpP5ubZDZEgGP9YqeStDTG9Vi4VWQ8IZ770kLfZig8b+APwR+T/nQdwLvkWX5a7/cB38952GBxvK/+VPaUouji7Nc/5tt3vkD5xmcOd3t0yqWSP/SL3H0B3+AwWbD/9734n/vd2P0nHQlN9tNXth7gT9b+zOe3XmWYqOIw+Tgyf4neevgW3my78mvHJtot4XFdfM52HpBAEVuW/ybySasrgOP6UDhunuqrSzLJPNVrm8fayAxv5ujqCR2Oi1GAQwDXi7093B+oIeo13Yq8BWbLeaLFa7nBUBcK5RZr+gv3iGbRQEIARLn3A48GkDcpFCY10CiWIprIyaj0YXJOEqtHuEo62Fn18jxkYnOcqDbAcLSNgnWsKcyCMWZohyD2yLYQ8yJpc9F0yNzeCi2p9XxUmdrnN3jpXdkVOgPQ2ewuWLUKg4yOyUy2wUy2x3uJQl8vQ6CA26CfU56bBVcuU1Yi1ONL1NbWqaZ7ujWjsWwTk9hm5zCNjWJeXycXVedleMVjT3cvhgXdUZ1cPBNMOGI0VfMYDhY0kdL6bjudlP3HjrGS9XANIm8RWMNKkDkqzoTGPQ7mFQBIupmrNdN3W5U2IMAiOVilWRdZxxhpQxqymnXOsfPOmwYNFtrXL+VEjQaehKt1RpVmMOkEKddk9jtw8jyyY3p24XpO7UI3i5Ma7bW2wCi0/5s9Fo7wEE4mExBO9IpGWRyu00udaCMlfTO8uMDfRyobt8HB0eUPRpRLmWx32ccUFumkK2S2SkyejH88OpeZVm+cLePPazzMECjuJfm+JfjHPgO+dK6h7mn+nnzu8dP/dzSCy+w9+/+Hc39JL5/8G6CP/ADp1ab3jy6yZ/e+lP+bO3PyFQy9Fh7+JrBr+Gtg2/lDdE3YDV+BeJHWk3RCbH5vLhtPa87mtwxGHyDMmp6TIwRTHffL6k2Wszv5riyecSVrSOubh2TUuI2zEaJyYiH8wNezvf3cGGghzMh16llQeVWm8WiGC1dU0DiZlnP4umzmhVwcHDB42DObcdvNtFuNymVb1LIL5AvzFMoLFAsLnUDhOkM9VqUo2MPu7tmsofC4ipJEqFQiFgsRiwW0/YgjDWRXNypQbQ6tpuNPVadQcSc1Ow1Muktbbx0u0DtCYUJD48SHjlDQNEfSjkTmd0Sma0Ch3t6KZAarREccBOI2vG2szizt2iuxKkuL1OLx/XdB5MJ6+ioGC1NTWKbmqY9OsCt9oE2XlLjNVRx2mQwaYmtk/5JJnvGGZeseLMb+mjpYEG/eAB9a1oZLRGZI2UbZOmgyvK+AAex96BrD06LkUnFsaQCRNjvYLPZYLlYVdhDhUTHUpxZkhhTusbVzg+VPdRq+3qUu+Je6i6C6rC1uqc0DcJk8pwqTGcyGVqtlvK1YpP+doA4IUzfo61Vj313KP3kDgx3WO6tlcsddbTrJ5J/tewuZcEyqMTDe0Lh+54w1KtNkfe1q9iqd4oc7hVpVMXP4f2/9taHBhp/Dfw28EfKh/4B8I9lWX7rl/vgr+c8DNBY/aNnsF838qVmlqojzN//scdOFCjJskz2N3+T1C/8IpbhYaI/9VM4Ll3s+pxGq8Ffbf4VfxT/I66nr2OSTDzZ/yTfPPrNvLn/zV9+AmyzJvYiNp8TILH9op7O6T8DQ0/A0BvF/T1YXmVZZi9X1QDiytYxS3s5bcw06HdwaVCAw/mBHqaip+sQbVnmZrnGlXyJK/kyV/NllkoVzRMftpi4oACEOmoKWcy0203K5VsaOOTzCxSLy7Tb4g1RNMidpVGPcnzsZXfPTCat7puKHQgVIGKxGJFIBEO53aE/lKjvFmkXdDZjCto19mCKOigZCqQPNjX2kNpYo1oQV6eSZMAX6xMC9cgoPZEhJENIEajFeOn4QO9ntjpMBJXxUiBgxF09wJpM0IgvU12Oi8a4pjJScTiwTk1hm5zENj2FdWKS45ibldI6iaOExiC2Cnq8itfq7R4vuYcUa+uyGCslFQahprxKBgiMdbCHORqhadYqbpaTQndQASJT1H9GfT12rWZ2OupmPOKmYTNqURpLyv1eh5U5aFbYQ0ff+FmHFUO7Qqm0ottai3GKpfhteUsDuFwTmu6g2lqbzTaZTIZkMtkFEOWOzu7bhelwOEwwGDwhTLfrre6xkmprrb6GrTXqxOS3nWprbbdbHCeTykhJ0R42N7p6Q25P/g0PjRAYGMRsvffWRxDsIZepiJ2bjq39fEZ3XVnsJnFx0qcsZ/a5iI72PDTQGAR+BXgcgbfPIzSNzbt83X8HngZSsizPnvLvTwH/E1CztT8py/KH7vaEHwZozH/oUzgKTj6dN/KtH7hE30Q3c2jXauz/6I+S/8tP4/7GbyD2Uz+FwamLTulymo+ufJSPJT7GYfWQIc8Q7xp/F0+feZqA/d4W2k49rabYjbj1eVj/W+FwUovnw9MKSDwBg0+AJ3rXb1drtljYzXN1S4DEq5tHWsSCzWzgXH8PlwZ9XBrs4eKgj5D7dDaUrje4mi9zJV/mSr7EtUJZ88W7jQYueBxc8ji5qLCIiLIHUS5vkM9fV0BinkJhWfPEC4AYpdmIcZzzsrdnIXUAKkAEAoEugOjt7cVUkk8wiHbHCMgUdmj6g7HXRr4lFuRSG7dIrYsdiEZNsZOqAvXwGULDZ3D5+pHloNh/2DmpP7h8VjFeGnDhd7dxFbcwbixTWxa3xp6eh2QKhwVzmJzCNjWFeWKcPW+L+LHQHZazy8SzcY5r+h7DgHtAHy35J5i09dKb20dSdYfkvOgxVxfjLG7BHCJzGkjk3GdZzjQUcVoAxMpBkbryu7IYDYxHXExFPBpI9AUd7LRbGnNYLFZIlPSuBzVSQ2MOSjBjyGLsKALS3UvdSb3ODseS4l5yjp/IW1JBIpPJoL5fmUymE8J0b2/vSWG6LdM6qp4Ah2a2qrMHq/EEOJh7HRhsp+t51WJRGy2pIJHZ3qJZV1oHlYsLtVQqNKTGwwfvmz3Uyo1u9rB7W6yLBN6wQ9+9UeJd3H4xEpYbDeobG1QTK/S88+n/s91TkiS9GSgCv/saoPEjsiw/fT/f90GDRrvZYu3f/jWp6iHVRy/yNd/V7XhqFYvs/PPvp/zSS4R++AMEvvd7tT+EZCnJb8z/Bp9Y/QTNdpMn+57kH079Q56IPfH6qktlGbJrcOtvYO0ZWH8WajlAEqmuw08qIPE4OO4eM3KQr/LqpgCHK1tHLO7mtfz/fp9dA4hLQz6moh7Mp8xjK6028wUFIAqCRahCtVGCKaedSx4HFxWgGHOIqI1aLS0AQr0VbmhXlwaDHYt5lEYzRu7Yx/6+mWRSdzH5fL4TDMJcM9DYKVDfKVJX7rUdCLX/QXExGSM2co1DDjZvcrC2ysHaLTLbm5pAbbbZCQ+PCAfT0BkcPX006l4Odyuktwqktwqa/iBJ0BNxauF8fkcNx/Em3FqiuiRurbQyulKC+WxTU9p4SRoT7qXl7DLxwzjxozirR6tazIvZYGbMN6YBxJRvgjEsuA5vdbCH+e5QPk9fB0Cco907x44cYilZYElxLi3t5bvKgAJOSwd78DAecWN0mUhU6ix31Ml2LkL6zUamnfpoacZlY8xpw9iuCHAoqM4lUQbUaqluObEU51bsrKr2YLP10Wy27soe1IpZ9RaJRPD7/V3CNChLcSfYQxm53lKfBqaA/YRzydhjPZ09tFoc7e91FEoJ9lA41PUlm9tDWNUe1Gra/kFM95ky3W7L5FLlDmAokdkpUMzqFyZarIvCHoL9LnxRpzYFaR4eiv0bpb2wurJC/eZNrb55OhF/4M19/0qW5Z+TJOkjnNLgJ8vyD971m0vSMPDn/zeBRvLlOM1PpLla3uZrf/pdXcm1zaMjtt73Pmorq8Q+/B/wftM3AYJZ/ObCb/KxxMdoy22+ZexbeO/MexnyDN3/EyhnBUCsfR5uPaPHgfcMwpmvhtGvhpG33BUkZFlm47DMy+tZXlzP8vJGVuuGsJgMnOvzcmnIpwFF2HOSIrdlmVvlmsYg1DGTGp7aZzVr4HDJ4+Cc24FDKQsS46Xr5PM3yOevU62pb3JGrJYRWq1B8vkA+/tW9vZ0gPB6vV0AEY1GsbZNAhy2C4JF7BT0BjmDJCI2+t2Y+1yYonYBEBsdALG1TksZA9mcLsJnztJ75izh4TPYPX1CoN4qkdoqkNnWAcJglAj0uQgNukVznKWEI7NGc0UBiMUlvXPaaBT6w/S0uM1MUxuJslrb0ZhDPBtnPbeupQm7zW5ttDTpn2TSc4Yz9Y7x0v4NoT+oI0fJCKGJDoCY08Rpday0tCdEatWYYJCEvXk65mUq6mY66mEo7CRFm6VyjcVCReubVpN6jRKM2m1Mu2wdAGEnrHU96CVQxeKyEqkhjsnk7mAOys05hsFgv2f2oAY13jFv6falOAUkOjfrJZsJc9SBJerSR0u9Dgx3ak/M5zRQUEulDne2aClvuAajEX/fgLLzoMfDO3t8980eqqVGV5zL4W6xS/eSDBI9vXoopMoinD1iZ0Ou16mtr1OLx6kmVsT9yooIN1V/D+GwCImcUCtuJ7BPTjxw0HinLMt/JknSd5/277Is/85dv/ndQeMTwA6whwCQxbt9zwcNGlf/458SyvhIXvby6Lef0z7eyufZ+sffQ211lf5f+QiuN7+ZWqvGr9/4dX5n8Xdotpt889lv5vvOfR99rr57f0BZFmOF+F9A4i9h5xVABqsHRt4sQOLMVwuN4jX+ONttmcRBgZfWs7y0keWl9azWD+F3Wrg87OPysJ9Hh/1MRz1YTCdZRL7Z4tVciZdyQou4VihrnRAuo4ELbgeX1FGTx0GvVegQpdJqF4sollZRBUyzOQYMUyqGSR7Y2dmWaLXEC9ftdncBRCwWwy5ZqO8Wqe8UNSbRyilvBhKYQg4s/S4s/W5MMQf5dpbU5i2SawIk0pvr2gvd6nDSe2aU3jNj9I6cxdEzQKVoI71dJL2VJ71VpF5R3lxNEsE+F8FBN6F+Jz5jAXv6Jo34ItXFJarLy1oxkGQ2i+1pBRysU1Pk+ntIlNd1BpGNd5UChe1hJgOTOkDYo/QX0t3jpXSiY7zk6gIHInOk7CMspeoKQBRY2st1WVtdVhOTEbfGICYjbrw9Nm7W6xpzWCxWuhxqPSajxhqmFHCYcNgw09C0h4ICEsVinGazMxZjCJdrSnEuTeFyTWGzxWg2myeW4pLJZNdS3D2zh7K+FFffv9tSnEu3tXotp76Zt5pNsns7XTsP6c11Skf6UqLD29PVWR4cHMbfN4DpPuuQ2602RwdlAQo7+oipM1Le5jJr7EG990UdmBStsJnJiFrbuNJBEk8ILUzd5LdYsI6NdQDEJNaJ8VPNOA/TcvsuWZY/dreP3eFrh7kzaHiAtizLRUmS3g78kizLY3f4Pt8HfB/A4ODgI5ubrymnfFnn2g9/ApNsZPzDT2NRZprtUomt930vlcVF+j/yy7ifeoqrqat88LkPspHf4O0jb+f9F97PgGfg3h6k3RKitQoU2TXx8dhFGP8GGP0aEej3GjsSjVab+d0cL61neVlhEqr1Mea18diIn8sjft4w4mc05DrxAlKb5V5WQOLlXIl4qYp6zT/lsmngcMnjYMxhwwBUq3vk89d0FlFY0HQIo9GLyXSWaiVCJuNma0vPYrLZbPT19Wm3WCyG0+JQROqCBhLNQ13MMwZsWPrdQqTuc1CS8hxs3+Jg7SbJtVXSG+vaHNlitxMe6QAIbz/Vsp30tnAwpbcK1BWRU3UwhYY8hGJ2vNIx9tQqjWWFQcTjyFXxPCSbDdvEBLaZaWwzM1imJkn1Wonnb7J0uMRydplENsFRTbjUJCSGPEM6OPgmmLT0EMhuiZ2Y/evC4aZV0iKcbZE5MXKMzNEOz7Eph1jcL2hVs0v73SVRIlZDCNPTMbEYV7MZWCpVWejQH7INXdgdtlu6iqCmXXb6rGbq9YzCHHRwEHsPys/L6MDpnNDBwS1yl4xG51eOPbRkmhk1rbUsQhuTJVq5jqU4h0mPXbnLUhxA6fhIAwUVJA53trWxpNFkwt8/KHSHwWFCQ2cIDg7h7Lm3pOXOUynUdVFaEaiz+yXaCi03GCV8ESeBfoU5KCMmh8fSzR4SCjCcxh56e0XES0dJlWV4+K7Bps12k638FqO+0YcGGldkWb50t4/d4WuHuQNonPK5G8CjsixnXuvzHiTTKKSOyf6na+wZUzz+4b8HgNxssvP976f47LP0/dJ/xv22t/F7S7/HL7z6C0ScET74VR/kib4n7v7N220BFPMfg6U/gfKh8MKPvBkm3w7j3wjeOzOUdlsmnizw/K0Mz93M8NJ6lpIyqz0TcvKGET+Xh/08NuKn33fSy11vt1koVrpAQq0edRkNPOpxctnr5DGvAAqXyUirVSafv0Eud4Vc7iq5/HUtsE+SLFgsozQb/Rwf+9jeNnN4KJxMBoOBSCRCX18f/f399PX14ff4xBtChwbRTOuLckavFbPCIMwxJ2VzgdTumsYgUutrmkhtttoUgDirA0TFSWa7JDSI7YJmMzSaDAT6XYQH3QRjdrztDPbkCnUFIGorK9rM1+B0YpuaEgAxPY1laoq9gEQ8t8LS4RJLh0vEs3GKDTEuMhvMnO05y1Rgikn/JFM9E4xLFhyZVR0g9q+L3zUI91JwXNMeiMxRC06zUrCxtJ/TqmaX9/Pa79ZkkDjbURI1HfUwEHay3WqKjvFCRWuLUxfj1MRWFRxmlVgNkbm0poNDQbCIzhBGqzWqu5bc07hdk9jtQzSbrftiDypInMYeWsX6CXBopMp6aZRBwhw+yR4MbvOp7KHZaJDd3VYSf/XMpXJONxK4lFh41dIaGhzGF+vHeI9J0urR2MOObmvN7BQpd2x8OzwWLfNLdS75Ig6MCru/J/Zw9qzY5L8Le7j9HFeP9aywoxUS2YTWdLjw3oUHPp76RuDtwN8D/rjjnzzAtCzLj931m78204gAB7Isy5IkPQZ8HBiS74JiDxI0rv7G5wjdtJCdg3PveRKA5E/9B45+//eJ/PsP4vr738GHX/wwH1/5OG8bfBs/+cafvPsiXmoZrv8PWPiE8Mab7DDxjTD1Tjj7tjt2WKuaxHM3M7xw65AX1g7JlsQf5pmQkydGAzwxGuTysP9UV9NRo8krCji8lCtxvVDWsnoGbBYe8zp5VAGJSafOInK5V8nlr5DLXaFYjGtXmxbLILI8TLEQYj9pY3cHLY/J5/N1AUSkNwLZOvWtggIQBRrJsrYpa3CZNQ3C0u+iYimRSq53AMQtLebbZLESHj4jNAgFIOpVN5ntEqmtPJntIg0l/dNoNoiIjUE3wV4L3lYG216CelwBiJs3QfXue73YFXCwTU9jnpxkx9skfpzoAgg1XsNqtAphOjDFdGCaqZ5xzrZkzAeLQntQGURNGd8YzCJaI3peu+Xc4ywdtljcy7Gk6A83U0Wt88FpMTIV9WjtgdNRD3avlZvVOgsd46XOUL6A2cSc2jPuFiAxarcit3L63kNBFadXOzKXLLicY2LnoSNWw2TyauyhU5x+Xezh9kgNBSDaBV1cN7jNtzmXXJhDdqRTxqeyLFM6ynZYWtdPpP6azBYCA4OapTU4OEJwcAiH5/6LxTq1B5VFZPdKtJp65pcvqpgiVOdSTLAH4CR7SCSoJhIn2cPEuLbFf6/sodFusJnb1AAicZRgNbt6oqtEDZMc943zTWe/6YGDxnngAvAh4IMd/1QAPi/L8tGpX6h//R8BTwFB4AD494AZQJblX5Uk6f3APwOaQAX4gCzLz9/tCT9I0PjSv/ljIu0QkR97HJvHTvYP/5CDD/0k/u/+btw/8oN84JkP8Nzec/yTuX/C+y++/86OqHpZsIlXf1uwC4MJRt8Kc98BE28H6+lAU6m3eGEtwzOJNM8k0ppwHfXaeGI0yBvPBnh8NEDUaz/xtel6gy8dl3j+uMgLx0XiJWXZS4JZl4PLXgeXvS4e8zqJWM202zUKhSWdReSuUKsLT7nBYMNkGqdW7SOd9rK5ZaRa0QP7OgGir68PW9ssAGK7QH0rL5xMypWyZDNpGoS5z0nD1eTg4BbJW6uaUF0rC63AaDYTHjpD7+hZwsNnsXv6adTdZHbKCoMo0lQAwmQ2EBxwERr0EAib8FQPsO3HNQZRX1/XtrONgYDGHmwzM5gnJ9h0lIkfxcWI6XCZxFFCczDZTfZugPCeFfsPB4sCGPavi/0H5fMx2YWtNXoeIueQo+fYs4ywlKop4yUBEjtH+lV5yG0V4BAVDGIs4qKqjJcWixVlxFTVNCU1pVfdeVAZRMhsoFrdEgBR0EdM3YmtAdzu6dsyl84gywbS6bQGDslk8stjD/sdwvR+8WSkRmfXg6o93CGWp9locLizpYjTawpAbFAp6JqKOxjqsrSGhkbwRWIY7rP6WG7L5NIVpYiqoAFFp6Xa7jZruoMACHc3e+hyLsW/ouwhW81qGWHqrbPp0GQwMeod1cBhzDfGuHuEYOmwq8hK+q5PPbTxlBnxNzuJGCYkZPVy5X/DeZCgEf+RP6ckV3jkP72Lyo0bbLznO3E+8Tj+X/p5vv/zP8C19DU++FUf5NvHv/30b1BIwou/Bq/8JlRzYpHqkffC+XeD82SUuizLrGdKAiRW0nxp7ZB6s43dbOSJ0QBPTYR401iI4YDjBC1P1xs8f1zk+aMiLxyXWCkLkLAbDLzB6+SresS46YLHgdNopFbPCBahAEShMK9tVZvNUWCUQj7E3p6d3V0JMGhjJhUg+vv78bl7hCipAsR2QXetGCTRQz3oxjLgRgqbyRxts39rheTNBPs3VzTB0WA0ERoaITJ6lvDIKO7gEI2al8xOmdRGntRmQWMQJouBYL+b0JCbYMSKt36AZWeJ+sIClYV5Gpv6wpspGlXYwxS26WlMk+NsmHMs3wYQajmQ3WRnyi/AYTowzZRnmJFKCWNyXh8vpZb1WlGrR4yWoucgep5W7znWibGwX2JxL6fpD2qstyTBSMDJVMyjgcRQ2EVSarNQqDBfLLNQqLBSrmrTGbvBoDmX1BHTpMuGTRGn1fj2YmGJYilBq1VWHkupEr1NnLZaQ1QqFQ0UVIBIp9Pa1nTn3kMng7ij9qAK0wpAdLIHo8fSBQzm6J0jNUDRHjZEFW1GYRDZvR3a6nMzWwgODum21qFhQoMj2Fz3H7dTrzZPsIfb62xV55LKHoKvpT3cjT0oNbf3xB5aDdbz6ySyia6+ks44mJA9JAqslLTh8Z4xRgx2pemws8xqRQ+UNFohNIH0z7740EDj7cCvAbcQ4DEC/FNZlj/95T746zkPCjS2X1xF+lSSHc8hl//5U6x/mwCG0B//Lu9/+d8wn5nnZ978M3zD8Dec/OJUHJ7/CMx/VPyiJp+GN/xTsY1925t9uy1zbeeYzy4k+exiko1D8YIfDTl5aiLMUxMhLg/7T2xap2oKSChMYrUs3vScRgOPeZ080ePiiR4X59wOTBJUKlscH7/M8fFLHB+/TKUq3lglyYzFMkajPsBh1sfmhpFCQbyY7XY7g4ODDAwMMDAwQDQaxVBoKQBRoLaVp7Ff0hJdjV6rBhCmfif5dpaDjVX2bybYX01wuLutXe37ojEio+NEzk4Q6D9Dux3gcLfCwUaBg4281gNhMEkE+930DnsI9dnxtg6x7i1TW1igurAgRkzqKCISwT43i21mFtvsLMaJUdakQ5aySxpArBytaFdkLrOLqcCUBhJTzn6GSsc6QCRvKAtyijPH7hdlUhEBEM3ec9xsBlnYK4r+8V3BIMoKq7IYDUxE3Np4aSbmweezs9ZosKD0eywWK2x0uJfU3KU5l50ZtwCJYbuVVuNIEaeXFAZxe4WsS7AG97RyP4XTMYYkiSrR2wEip1qDAafTqbUGqgARCAS6eqZBdy7VOxnEQUnXHjoD+bSbS2uKu/20mg0Od7bJbG2QUkZLJ7SHQFCpo+1gD9EYBsN9sgdZpnBY1WpsDxUW0bk13VVnq7AIf8ypO5fulT109J9bJybuiT1kKhmto0RjD7lbNJU3elUvG/ON6ZH0zgH8hYPuGtyDBT0qCMDTr3eVqJv//lEwmh6qeyoOPC3L8k3l/0eBv5BlefLLffDXcx4UaLz4M39C33GA5tNBjH/4KxSffZb+3/1t/mXqv/Lqwav83Ft+jq8dui2jMZ2Az30I4n8uRhQXvxMe/+fCHttxWm2Zl9azfHYxyWcWkiTzVcxGiSdGg7xtKsxTE2EG/N3idbXV5qVciWeyBb5wlGexKP7YXZ0g4XNxzuXAKEGpfLMLJNTxhMnYg9E4QakcI7nvYHNT1yJCoZAGEAMDA/icXiFUq6Om7TztkrLUZjZg7ncrIOGi7mpwsL9G8tYK+6sJDtZvanHfNreH6NlxIqPjhEfGMFlj5FJtDjbypDby5NQeaiWor3fYQ2jQhc+Ux3GwQmN5gcr8ArV4XBOpjT4ftrlZ7LNz2GZnkabHWDNmWT5cZikrAGL1eFV70bktbsEe/AqDsPUyUExj0BjEDVFPqx53TNEeBEDUQ3OsVDws7OVZ2MuxsCsE6poyz7abjUzHPMzGPMz2eZmOebC4LSxXahpALHSUQIFwL8267My5HMy6BVCELCaq1W0KhWUKxUUNIDrHS1ZrBE34dxsAACAASURBVLdrGpd7CrdrBrd7Cputn2azRSqVOgEQamKrGs54O0C43d2Nk3JbppmtipFSB0B05nFpcd4d4HAn7QGgnDvWgUG5P9zd0Z1LZjOB/sGOznIBEnb36Rrfa51GvUVWWYbrjNZQ3XJI0NOxNa0ChcvXufewoQPDaewhHNY0B+uEGDFZRkbuiT2s5dY0UVplD9mqbvEN28N6T4lvgnHfGENtw8me9OytjjIrh0iB6KjCpXca7HcGrIcJGn8ry/KbO/5fAr7Q+bGHeR4UaLzywx/FJTkJPVYl9cEfI/Sv/xU/N7rMp9c/zYff9GHeOfpO/ZNzu/DMT8O1PxCdE49/v2AWty3cJZIFPnllh09d3SVVqGE1GXjLeIhvnIvwNZO9eO36FZksyyTKVb6QLfBMtsALx0WqbRmzJPGY18lTfjdv8rmZc9kxSm2KxThHCkAcH7+sFdqbTEEkxsnletnaspFOGwEJk8lEf3+/BhD9/f1Yqgbqm3lqm3nqGznRC6HWUoftWAY8WAbdSCEzmcI2ybVV9m+KUVPpWFzdGE0mwiOjRBSQsHsGKBfspDcFg8julmgrc22Xz0p42EN4yI3fUcWVvUU7LkZM1aVlrQfC4HRim5kRIDE3B1NjrNnyLGWXNZvrreNb2pJcj7VHAIN/iunAFFOWAP25A6TkjdMtrr5hTX8geoFqcIZ40c7Cbo7FPdEemEgWtMwtl9XEjAIOs30eJqNeGg4jSyUBDAtKlWxR2a43KSVQAhgcmkDtMjSVdN5lbbxUKC5rDYFgwOkc7QCIaVyuKSwWP8ViUQOH06ytFotFGy2pt1OrRGtq5lKxazFOrt+296C4liwKQNzJudRqNjna2yG9ud7FHtS/D/F773AuKSDhi/bdv/YgyxSPal2BfJmdIrmUnvdlthk111KnOG223oE9JFa6GwzNZixjZ5XRktJkeA/sQZZljT10upfWj9dpKpHtFoOF0R5de5jwTTDmjOHL7Yuk4YNFJVByEep6Fhe+kdvAYUZ87B7i0NWTLdUJuKwPDTT+GzAEfBTxlvIuIAE8Bw+/9vVBgEatWGHvQ89zIKfwff4XsE1N8ckfvMB/X/otfujSD/G+ufeJT2y34aVfh8/9hBhDXf4n8OQPg1PPk8pVGnzi1R0+cWWHxb08JoPEUxNhvuVijK+eCOPsqGksNFt87jDP57MFvpAtaHHRYw4rb/G7eYvPzRM9LhxGA+XyGtnsF8kePc/x8YtaBIfZHEOWz3J8HGJzw0o2KxJeXS4XQ0NDGkj0hnppp6vUN3IKSORpKSMhyWrEMujGOuTBPOimZMqzv7HC3sryKWOmPqJnx+kdHccbHqbVCpDeVnSIrYImVFvsJnqH3YSHPAR8bTz5TaSbC1Tn56ksLtJWxiWSxSJsrnNz2OdmMc1MsdXTZCG7yEJmgYXMAjePb2odEH6bXwOImcAMU1Y/0aNdpL2rsHdV1NKqFlckYXHtYBBl/zTLxwbmd3KCRezmWE0Vtd5pr93MbJ+H2ZhoEByNuChYDZo4vVDotrfaDQZmXDZmlW6PWbdYjjO2ixSLS4pALe5FY5xaAOVQNqbFeMntnsbpHEeSLBweHp4AiGJRb2RTxelOgOjp6TnR96Altu7rING5ByPZjAowuHQG0eu4495DOZ/THEvqiCm7s6Vt26t7D7ePl16Pc6nVaJPdF+wh07H7UCvpzM0TtHWwBzeBfheegAgU7GIPir21upLQI17o2Jqe7GAPw8NId1niq7fq3Dq+1QUQq0erXeyh19Hb5Vya6BlnsC1hSi/rScMHC5BdR7tSs3q6anDpnRUOvDsYZ047tWaLW6kS8aRIBljez5NIFkgVamz+7EPKnrpD3at6Hnrt64MAjYX/8Rw919psZJ8n+MpH2fmvH+BfJn6Gd42/ix//qh8XV1i5Hfj4+2D7S3D2a+Ed/wl8ekzIykGB33l+g09e2aXSaHGu38u3XezjnedjBFy6JXa/VuezmTyfzeT44lGRhizTYzLypM/NU343b/G76bdZqNXSHB09rwGFOq6wmPtot8c5Ogqxvm4mlxNvFG63m+HhYYaHhxkaGsLn8tLYLlLbyFPfzFPfKmiOJqPXimXYg3XYgyFq47C4w95qnL2VZfZW4lrtqM3lJjo2QfTsBMGhsxiMvRwl2yTXc6Q28lQU8dNoEk6m8LCHYMiIt7KLeWOB2uIi1fl5vQvCaMQ6Po59VmgQttkZDqI2Fo/jGkAsZ5c1kdpr9TIbnGU2MCsAwh6h92gHaV8BiN0resugZBQvsNgFiAiLa6FnnMVMW2EQeeZ3c13x3gGnRWMPszEvwxEXh0aZhWKV+aLoGe+Mb/ebjcy67My6RHT7rMvOiN1Cq5EW4nRhQesXr1b1jjKLJaToDjMaQNjtgzQaLW2ktL+/TzKZJJVK0VSTbw2GLmuren8ilK+z72G/RH2/SGO/rGdxoSxKRjv2HtTMpVPYg8hc2tWYgzpiKnZsTTt7fBowqCDxevYeAEq5mi5OK8L0UbKMrIYimg34bxstBftcWOzise6ZPahLcffBHtKVdNdYafVotSsKxmq0crbnrAYO475xxp19eHN7SpFVx3hJtWMjgX9EBwZVe+gZvGsSdedzS+arxPcLxJMFARL7BW6ldQu3xWRgLOxiMiLSAb7vLQ9pue//tPMgQOOFH/sofY0w2b/6Uezvfzf/yPYHjPvG+a2v/y0RX771Ivzxd0KjAm//eeGGkiRkWeYLK2n+32fXeO7mIRaTgW+5EOO7Hh9mtk+/urpVrvIX6RyfTue4WhAjmBG7hW8IevmGoJdHvU7kVpnj45fIKkBRKq0AYstakqY4ykZYX7eRy4mrIK/XqwHE8PAwHrOT+rpgELXNPI29oriAkcAccQqQGPLQ6GmR3L/FXmKJvZVlUhtrmkvF3zdAbHyK2PgkntAIlaKTg/UCyfUchztFbQTgizjoHfEQHnDSwxG23UXq89epXL/e5WSyjIzoOsTcLMWhEIvFVeYz8yweCiaRr4sXks1oYzowLUAiOMuse5j+fApp/5oAh70rortcPYExUUUbuwSxixx7J1hMN5lXBOrFPdEep55ej5XZmJcZpX+8P+wkJbW5UawwX6wwf1sBVNRq5pwyXlIBImoxUavtkC8sUlT6xQvFpa5KUYdjRHEvzSg2V+FeKpfLXeCwv7/P4eGhNl7q7B5XAeK0SO9Wsa63CSoMopmpqPo4ksXQbWtV+x6sp7+ZV4oF0hvrZLb08VJ35pKJQF+/FqsRVMZLDm/Pa7yiTj+tVpvjZLlDnBYsotLhvHL5rCfEaW/YgcEgIbdaIrE1Hhcb0/EE1fhyN3vQ+s9F3tL/x957RzmWWOW+v6OcYymUKudc1bkneWY8TnhsY2ywMSYY7mXxCLYvJjzC4+HrBTxYwCI9PwwYfC/GZsARg/N4xmFid0+HiqqcSypVSaVSlkrhvD/O0ZHU3TPdPTNuj6H3Wlpa3e7qKldP6advf3t/W5lcuoF6KJQLLB8uNxjTi/HFhqThZnNzDQyufvod/XSIAupIsKYcdmfkhIfqfV5rnSk9Ar6xW1YP2aMSi5E08+Gaerj6dG6Lw8ig38pgs5VBv3TfpNNtRlM3sXY7PY0u4H1AJ6D8lyeK4g++1E/+Yuq7AY3pX/03yuUjrKFP84EfzZEspfnUWz6F1+SF6c/A538eHG3wrkfAO4goijyxFOXPv7HI5c1Dmu0GfvLuDt51uh2XWeohhwtHfCFyyOf24kylJOP3uNXEGz123tBkp9+kJ5fbIBp9nP3oN0gkLiGKRQRBh1Y7TDrdxsaGid2wNPFst9vp7u5WIGHVmCisJSisJCisJqQzpEiGta7dik5uNSWFA8Jr84QW59lZmCMVld71a3R6/L19tAwM4+0eQKtvJr4rEl5JEFlLKD/IWoMaX6cNf7cdj0vEerhCJSgBIj8zq8RtqD1NmI4dwzA+jnFsjFJfB/NHmxIgorNMR6eJZKU9ELWgps/Zp6iIUUcfPbkMmvCkBIfQZYguofzgOdolOLRIgDiwDTMVrTArt5emdxINOxAtDmNDi8nvMRFCSuedSuWYSmfZztd+4NoMOsatRsZlQIxZjbg1grQ9LYMhlZolnZ5T2oKCoMFs7lXgYLWOYrEMolabSSaT1wCifnrJZrMpN8erz3a7vfEgUNWcDkl3QIrhNEehTMMtELVdjzbQCIgXuvcgJbauNWxO1x+TqmYu1asHV0sras2t333Jp4vXtJbqYzXUGhWugFlRDVVQVANCy+mMtC0dDEqtpfl5CktLyn9vaLVSQOTAQA0SAwNoXDcO8ozmosr52+rzRnJDUQ8GtUHadagCwtlPn6UV++HOtd5DofbvirNLhsNYDRT29pv2HioVka14lmA4xUJVPeymWI/VbsSb5dO51QNYg34bA35rgz/6fHU7oTEJ/AMwjfJ+BkRR/PZL/eQvpl5uaOwvhih8bIWVveeYesMWH81/g79//d9zpvkMXP4kfOGXpPjxH/0EmFw8vRLlz76+yHMbcQJ2A+99qI8fOdmKTqOiUKnwlf0EnwjFeOowjQgcs5p4u8/BW7wO/Do1icRlotHH2I8+Tja7DIBO18XRUT/hkJO1NRXlshqdTkdXVxc9PT309PRg11s5WktSWD2UIBGRIaFToeu0o++2o+mwcJDdZnt+lu35WUILQSV6w+JyExgYJtA3iMPfQ7HoYG8jy+6KpCKqZrXDZ8LfZcPbbsZZ2UO/NUthUoJEKSydoxS0WgzDwxiPTWCcmEA9NsyqPsl0bIbZmASI9cQ6ovyi325tVxTEmGuIgWIZY2ROAsTOZdibqwX1WfwKHAicIOkc5cqBmqntQya3JRURTtT68h1uk6wgpEkmT5OJzUqZqVSW6VSOqVSu4bRot1EvgcEi3RgftRqxqcpkMgvy/sMsqdScfPxJapOpVHpJPViHFUiYzQMIgpaDgwMFDFVI1Md6V0/L1kPCXHd7BUAsVihGMpKCCNcgoZjTKqTR1oBFUg4ByaB+vmtxR/lcLa11fZW9jVWimxtKTpdKrcYVaG0I5fN0dr+ozKX6SO96c7o+lM9k0zXsPLhbLTh9JlRqFaIoUgqHyct3zwtByYMobtZUpdpul8EwKD0PDaLv7ka4Qfx4sVJkPbGuXDisQqLee2g2NysjrdXJpbaKgHrvKu8htkJNPVgajWn/mDTJdAvqIZErKmAIhqXnhd2UMr4tCNDpNitgGGy2MuS30eo0orrOm4KbqdsJjXOiKJ59qZ/o5aqXGxrn/vAztCR8LOcf533HP8N7ht/Dr53+Nbj0cfj390kJs+/6Z0JZgd/74hxfmdnFbzPwSw/18s5Treg1atZzBf4pFOORcIyDYpl2g453+l28zeegyyAQi32H/f2vE419i2LxAEHQoNGMcHjYzuKikXRK6i23tLQokGh2+yitpSisJiisHkoxHMhKotOGvseBus1ELLPN9sIM23MzhJcWKBWld6Ke9k5ahkYJ9A9hsLaTjGoILx8SXk2QlUPgNDoVvk4bvm47TfYStvgyYlVFBINKT1gbCCiAMIxPsNtqYjoRZDo6zUx0hoX4gjLq6ja4GWsakwDhHmYEA/boktxiuiz1eauHo4xOpb1EywlynnFmU2Ymt6Xb41Pbh8oeC0gR32Nye2mkxYa/ycRqqcSknMg7mcoqeVoqpONA47JyqLaZTEJB9h+q7aVZ2aCWPk6K9h7Gah3BKj+bTN3SufX9/Qb1EIlElPHWqv9QDwifz4de3xjxUs4UJVM6JPsPITmDq9pe0svmdED2HgIWtF4Tgvb6sRrpeIz99TX21qtb06vEd8PK4ILBbMHT2V0DREeXdO/hFhNbAQq5Ul3mkqQiDkIZSsXqSVYBZ7NJVg9WBRDVWI3K0RFHy8tKW6kwL422VupUmLajXTpONTiggELj998wfjxRSDSAYeFggeXDZWVHp7r3MOAaUA5Z9VvasCd2aqqhCoj8VeqhCoYqKBwdN60eSuUKa9EMwd0U87IpPb+barhtYjdqGaprKw34bfT7LJh0t+4PvVDdTmi8G+gDvg4obx9EUbz0Uj/5i6mXHRq//AncWg+/MvBHqD0O/uXN/4J+8VH41E9KabM/+kk+PbnPB/99looo8r6H+vjv93Vh0Kp5LpHhLzciPBpLohbgDW47P9Xi5j67gcThM0QiX2I/+nVKpRRqtQ0YJRLxs7Soo1TSYrFY6O/vp6+vj86OTtSxEvnFOPnFOEdbSajUQaLbjrrVyH56k+2FWbbmZthdXqRSLiEIKjydXbQNjxLoH0Fraie2U5IgsZJQwvusbgPNPXZ8HRaclT0M65Pkr1whNzmpzKQLBgPG0VGMxyYwTEzASD9BYZfJ/UnlkZAluVlrZsQ9IgNilFF9E77YGsLORXmSabJ2C0JngeZj0CIpiKL/GIsFF1M7SSa3JBWxGEkpU0x+m4HxVjsTbQ4mWh10+MyslUrSjXH5znj1QJAA9Jr0yn3xCauJYYsBvZiXW0sz8mO2YUFOq3Vjs45gtY5gsY5gs45gMLRxdHREJBJpAMTe3h4VeamwOt5aDwiPx9PgP4iiSPkgr4ChGJaUhBLzjrw5Ld8h1zZb0AXMqJ3Xby9VI733N2RAyBvU+bpYDbvPj7ejG09nF56ObrydXVjdnlu+99BwTlQ2pqPbaVJ1k1cGs1ZRDlU4uPxm1DLcSvG45DsE5yVz+qrztoLBoGxNG4YGpViN/n7UFvN1v6ZqVcQK26lt5QTu4oFkUIczYeXPuAwuBpzSnZJ+lzS51Cno0O7NN7aX6vcedBZJLVRNad+otPegtz7PV3JtRdMF2ZiuqYelvdplRI1KoMdjUXyHqnrw2a4/kPBy1+2Exh8CP4m0EV5tT4miKD70Uj/5i6mXExrloxJr/9djRPO7/PzpP+eRNz3CUCYBH38r+EbJv/vzfPAr6/zrc1vc3e3mj39knFankSfiaf5iI8LTh2lcWjX/rcXDTwTcWIprhMKfZnf33ygWD1CpzFQqE2xt+tnYMCKK0rvRgYEBBgYG8FubKCwdkl+MU1g+lE6TCqBtsWDoc6LrsRLLhdgITrIxfYXIyhKVchlBpcLf3Ufr8Cj+3iHU2hai20VCS4dE1pJKoJorYKa514G/RYczt4kQvEzu4kVy09OI8iKetqNd8iImJCURaTYwFZ9lck8CxNLhkjLu2m3vZsIzIT2cA3RnDlHtXJTOzm4/Byn5B1etl0ZcZRUhBo6zLrQwuZ1kcvuQKbnNVF2Usxu1EiBaHYy32ulrtrKrEplMZhVI1JvUnUadBAj5zviY1YiRrLT/IAMimZohm60ZkjqdF5t1FKt1FKttFKt1BL3ORzabbYDD7u4usVgt9dVkMilgqELi6uwlsVShuJdV/Idqi0ks1F2M85iktlKgbnrpeXKXCtmMpB7kzKW99VViWxu10VatlqY2aZzV29klKYn2LvSma9ONb1TFQlmBQlVBxHYySoSLIFA7CKSY01bMDjlWo1LhaGOjwZguzC9QitRuYyuLcYqCGELX0Y5wgz2NbDHL0uGSMr00fyBdOayGSKoFNZ22TqW1JN1Jb6cptV+bWKq2mPI1QxtnZx0YZO/B0XnT6iFfLLO8l5amlsJJFiIpguEU0XTtDYHXqmew2caQbE4P+Gz0eM3oNbe2m/Jy1u3eCB//XuZN1dfLCY3gJx/DOq3jieRjbP+MmV/vfQf83YNgcpP8sS/xM59e5eJGnPc91Msvv7afC8kMH1oOcTmVxa/T8gvtHt7tM5GKfplQ6FMkkpcRBA2CcJztrRZWV02Aho6ODgUUloyW3FyMfDCmtJxUVi2GPif6PidZU4rN5Rk2pi+zPTdDsZBHEFT4e/toH53A2zUEgp+9zTzhpUP2t9KIFRFBJeBps9Dc58DXBLaDRcSZS2QvXqSwuCi1K9RqDMPDmE6cwHjyBMLYEEHCioKY2p9S7kJYtBbGmsaY8E4w0TTOmNqGfS8oA+KC9MNY9SGcXdB6Wn6cImLq5UooK/kQWwmmtg+VWx8GrYrRgJ3xVgcTbXYGAzbSOoEr6ZwEiGSOpWxeGXNt0WuZkOFwzGZi3GrEKuRIpWZJKgpihmx2nSog9Hq/BAfrqKwkRtHpPCSTScV7qAIimax7p263X+M/2Gy2hneBlUJZai/tSMZ0MZSWYr3lRUBBq6q1lQLyDoT/+rsPoiiS3N+rqYeNVfbW10ju115wjTa7dKe8o0t5dgVaX9RiXDZxxP5WqsF7ONyrLXTqjJoG76Gp1YKr2YxGvnZXyWYpLC42+g+Li4jVgEO1Gn13t3TatqogBgdvypyOZCMKGKqQ2EhuKL6YRWuh39kvgcE1wICjnx61CUN0qTa1FJmB2HLd1rT52kgN7/DzJktf7+sKJ/J1ykGCxGo0oyhivUZFv88qTy5JkBjwWxvG7F8pdTuh8a/A+0RR3HvBP3ib6uWExpO/8g906vr5A8+H+dOf/zDmf3obHG4Se/fX+PHP7bO6n+Ev3nWMkV4Xv7cS4ov7CQJ6LR/o9PFWZ4m90D+xs/MIpVICtbqV6P4gCwtOikUpCXZsbIyRwWG0e2UJFHMxaaFOAF2nHeOgk4pfzXY4yObMFTZmJpVAP2dzC+1jx2gdGketb2Nv/YidhTj7WykQpekTX5eN5l47HlMWa2SO4uRFchcvUgxJF+MEkwnTsWMYT57AeOIEBz1uJlMLCiSW4kvKxEiXvaumImw9dKdjqHcu1VRETjYPdVbJqJYhkXRPMBnXMLWd4IrsQ0SS0jsutUpg0G+VANEqjbuWLWqmM3kmkzmupLLM152PbdJq5PaSUVERbk2RZGqWVHJKPvo03XBeVK9vrikI6whW2xg6rZtkMkkoFCIUChEOhwmFQopBXY3XqFcPfr//mv2HcqZYUw+hNMWQPN5aPftg1krx7gEZEs1mNG7jddtL1dTWfdl7qKqIgnwNEEHA2dyiTC15O7sVc/pWWxcNo60yJKLbafLp2kCArclAU6uVprZae8nqMkjqQRQp7e01Ti7Nz3O0saF4JSqrtWZMD0qx3vreXlT6F36xLJaLrCRWFO9h8WCR+fi80vIEaLW0NngPA9ZOAtlDhGoYX9V7qM9ccnQ07jzc4tZ0plBiIZJS2kvV52Tdrkur06j4DtWppU63qWGs9ZVctxMa3wLGgQs0ehrf9yO3l3/5U2hVWsLvN/O6S5+FqX8l8bZP8rZHzewm8/zNT57kiq7Cn67tohYE3tvu5aebckS2PsJu5N8RxTKiOMHCfBv7+zZcLjcTExOMDo1gigpkp/bJBw8QC2UErQp9vxPjkIuUKcnq7AVWL10gsipNUBmtNtrHjtE2Mo7J3ks8omZ7/oDIWpJKWUSlEfB32WkdcOAxZTBvXiH/3DmyF55TjER1UxOmkycxnTyB4cRxNr1qLsWucGnvEpcil9jPSeO2Jo2JMc+YBIimMSYw1qmI56RMreqSh2cQWk9B62lKgVMslgNc2k5yaTPOlc1DVut2IbqbzIoPMdpiR+eQspgmU5KKmE3nKFSntDRqWUEYFR/CrxXJZBZlOEiQyGSWqXZF9fpmbLYxWUFIkNBq3SQSCQUM1wOEx+NR7o0HAgF8Pl9DvIYoilRSRxztNCqI+uwltUOPNiADosWCLmBBZbv+SdF8Ji15DvJjf32V2M5WLbVVr8fT3ikrh268nd00tXWgNVx7p/1GVcgWie2k2d+qTS/FQumG0VZ3izzaWoVE3WKcWCxSWF1V/If8gqQgyoe1do62ra3BmDYMDqIJBG4Is3g+XhttlSGxmlhVhiYMakPNnJYh0a9zYomtyotx8inc6FJN1WrNktdQNaWrk0s3qR4qFZHNg2yD7zC/m2KjbuDCotdIY6116qHfb8VmuPXhgVdS3U5oPHC93/9+H7lNrIU5/JsFltNBHvpZG8IXfpH8fb/B22ZfxXo0w5/9xHE+mk3x9GGaN3ns/E6binzobwjvfhZQk0mfYHbWT6FgY2BggNOnThMQneQmo+RmYoj5EiqTBsOwG12fjd38OqtXzrN6+TlJTQgCgb5Buk+cxt02TCpuYXs+QWj5UIriEMDTZqV10InPXsAWnqJw4RzZ8+cpx6V3WNrWVkxnz2A6dRrdsXEWTQku7l3i0t4lLu9dJiXn1/hMPk74TnDSe5JjzgF60weot87D5jOwfbGWc2N0NbSZ4s4xLkXKXNqMc2njkMntQ2UksMmi43i7k2OyUe31GFk8KnIxmeFyMstUOkdWzmIyq1WMW42KD3HMZqJdryGbW5UVxDTJ1BSpVFA5EqTVurDZxrBZx7HZxrHaxtHdAiCqkLgeIMoHeUk57NQURKX6LlwAjduogEErq4jrJbdWjwLtra+yt7YiQ2KFxF6tvWR2uvB2diutJU9HNw6//6Wlttaph3pz2mjV0tRmlfYe2iRIOHxGVPI74XIiIZ8SDcr+wzxHy8tKKKSg16Pv61OMael5APUNIsjLlTIbqQ3FlK5Cov4gUDWUTzGoHb10FIuoI7ONgEjXvnfY2+SppToFcQvqIZkvMh+uLsMlmQunWNxNkZNP4KoE6GwyMyRvTFd3H1ocL36s9ZVctw0ar7R6uaDx+Ic+Sn9ukMuGc7xF9xdU/OO8K/9bXN5J8cF3jvMn6UNS5Qq/1+3mdPYf2d75OKIIqdRxZmfb0KjdnD59mmP9Y2gWcmQu7FI+LCDo1BhH3GgGbWwfzrPw7HfYmL5CuVhEZzTSOXGSjomT6E09RNaKbMzGlLhmh89E66ATf1MZ+/4c5YvPkj1/Xonh0Pj9mM+ewXT2LlQnx5nRRrgUkSAxvT9Nviz9PZ22Tk76TnLSd5IT5nYCsTWErXMSJMJT8rs2QfpBbDsLrWcoBU6ycNTEpa0ElzfiXNqMK+OuapXAcLON4+0OTrQ7GW61E9eIXErluJjMcCmZx4LzCAAAIABJREFUJSRPMukEgVGrkeNWExM2CRLdRh3FQkhRD8nkFKnUrBLUp1abJfVgG8Nmm8BmHUevDygeRH2bqR4Q1RHXKiD8fj/aulFSsSJS2s9KymEnLSmJcBqxmn6qkg8D1SkIbbP5utvTYqVCfDfM3vqKAon9jbWGWG9ncwBPZ490abCuvXSrVSqWiYez1/gPRzm5VSKnAyveQ5u18eZDpUJxe7thcim/ME8pVJswUjc1yapBMqZv9uZDppi5xntYii8p/+1pBA3dju7aWKuznwFzC65EWAqOrAIiMlc7YqXSgndQCpCsqgffyDUBoM9XVfUQDCcJyhvTwauOXjlMWgb9VoaabRIkmq30ea0Ydd87Y/p21+1UGimULi46pOt7GVEUbz3D+GWolwsa33nf39Nu7Mba8We4Elf4fzr+gY9Ol/iVHxrm/yumMapUfLh1i8rm71IsHpBJTzAz041e7+fuu+9mxNpN8WKM/MIBiKDvdaCfcBHKLbNw/gnWrlykXCxidXvoO3M3vt4JjvI+toIJdhbjlIsVNDoVrQNO2vqsePJrcOkJMk8+RXFbyi1Se5ownzmL6ewZVCcnmNbvcX73Ahd2LxA8CFIWy6gEFQPOAQkS3hMc1zhwR+Zg81kJEtX4b41RajO13wXtd3HgnOBSpCKpiM04U9uJa1TEiXYnx9sd2N1GZnN5LiazXEpmmE3XfIh2g46TNhMn7WZO2EyMWIwIpQNJPdS1maopvIKgw2oZlOBgG8NqG8dk7CKZTDeoh+sB4uoWUwMgyjIgqi2mKiCqC3IalZS91GKpTTH5zNfdfyiXikS3NiVArK0qOxDFvPQipFJrcLe1ywqiB29XN96OLnTGW59eyqWOZPWQVjaoG3KX9GplY7qqHlwtZrRVczqXo7C01BCtUZifp1JdMFSp0HV3NYy2GgYH0Hg8L/h1iaJIKBNq9B4O5tlO1zK17Hq7vBAnG9TOfroFPbr9RQkOu1NyKN9q7S82Oms30quAaOoHzQsv6lUrUygpURrVx8JuSrmprhKkfZ6hZhtDzdLRq8FmK36b4baMtb6S63umNARB+CHgjCiKv/1SP/mLqZcLGvO/+kVSxQSnXb/Ik6O/z08818077u3gs/YKPp2a3zf/K+x/klKplempcSqVNu5/1f0MazvIPRmiuJtFZdViOuHlwLzP7MVvsnrpAqWjAmani/6z9+LrPUXqwM7qlRjxsNT7t3uNdIy4aLZlsK5fJP/Ud8heuQKlEoLJhPmuuzDfew/606eYt6U4t3uec+FzTEWnKFVKaFQaxpvGJUh4JpgoCVhCVyRIbD1bS3g1NSmAqLTexaK6iwtbGS7JKmLjKhVxot3BiQ4nfQEb+2qRS6msAokDWc6b1SqOWU0NkHCq8tIUU3KKRHKKVHKKfCEkf5dVmM292GzjcptpDItlkEKhzM7OTsMjIxvCtwSI7TRHOymKO9IehCgvmQlalaQeWixSm6nFgsZjQlBf+6JxlMuyt7Emw2FFHm/dVO4+aA1GxZj2dkmQeDHLcVdvTke3pPHWTKI2lFifu9TUKqkHu6dmrJf296XJpWAVEPMcra8rR6lUZnODMW0YHELf14vqBl5JsVJk9XCV+YN55bEQX1DamwICHbYOJbV1wDnAgL0bXyYumdP1gKg3p13dsmoYk0ExBrbATYXyiaLIdjwng0GGxG6ywXuwGjSycrAqkOj3/ddSD7dS39P2lCAIz4qieNdL/eQvpl4OaFz63FfwnrcQTDzBmRPnOLn2c5zocXOlz4RLK/C7fBB9bortrWNsbY1z99l7OGbo5ejpPcrxAhqvCe1JOwuR88x861FSsX2MNjv9Z+/B03WS9IGL1ckoyWgeQYBAn4OOIRue9DLChcfJPPU0ZXkXQD80hOW++zDeezebnUbORy9zLnyOS3uXyJVyCAgMu4c503yGu7ynOV5RY9w6B2tPSKAoyka0qwfa74b2uzhqOct0rokLG3EurB3w3EZcCTdrsugVQEy0OTA49czlClxMZriYzLKYqY279psMnLSbOGkzc9JmoteoIZ9dkk7GJi+TTE417EIYDe1YbWMKJKzWEURRRyQSaQBE/R5EU1OTcmv8+QBR3MtS3EkpKqIBELrnAcR1etK5dIq91RUia8uyB7HSsD1dHW/1dvUoKsLpb0a4hbsFAKWjMrGdjNJeim6lGk6KSpvTZmVyqRrtbbBo5f/PcjBfcF7yH4ISIMp13zdtIIB+aEjKXhqSQKFtabnh15o+SiuLcdUWU/3mtFFjpM/Zx6BzUDGo+/RNmGIr0ljr7rS0ILc3XzuBqzFK5rTiP4zf0mJc7qgs7zpIymE+nCK4myQlTy4JAnS4TAoYpIfkPfxXVw+3UrezPfX2ul+qgFPAA6Io3v1SP/mLqZcDGo9+4MMM6ScIF/6QP/X9OBv4SZ31oNWK/K7421gL60xP34/LeZbX992H8OQB5XgBXbuVo164OPlFVi6eRxQrdIwfp+fUq8nnWll+TgKFSi3QOuiko8eAJzpF8YlvkH32WcRiEbXTifneezHfdy+54/08czTPkztPci58Tkl87bH3cKb5DGd9pzklmLDvXJIh8UwtXtkzCJ2vgs77yDSf4XJMx/m1GOfXD7iydUheflHtajJzutPJ6U4Xo20O9jUi55NZzifSXEpmlcNBTo2aEzazAoljViNGMUEieYVE4jLJxGWSqSnlHrVW68ZuP4bNOqa0mtRqO7FYrAEQu7u7yia1xWJR7o1XIWGoexcsVkRKe1mOtlMcbcttpnAGSlVAqNG2mNG1WBVIaJquP+KaTRwSWVthb22FyOoykbWVhv0Hm8fXoB68Xd1YnO5bfhHKZ4oSHLYkOOxvpTncrQXM1Z8UrU4v1W9ON+w+BOel5biFRSWYT4n1HhyqKYiBAdT2F75RIYoie9k9FuILyl30+YN5tlJbyp9xGVwMuYYYcMmLcY5+OioV1JG5OkDMQKL2MVh8NdVQBYS7B27C2K/uPVRTWudkSKxHM0pcvVmnliaWmmvqYcBnbbhDc6deXN1OaNTf0ygB68BHv1d7Gy8HNM6//5PYtA5W27/Ke3d/AP/9AaJmgQ9WfoumQoipqVdz1/Bb6Vu1U9rJoG02k+ktcO6ZzxFaCmKw2hi5/3WYHMfYmCuzt54EAVoHnHR3qXGHLnD0rUfJTU4CoG1vx/qa12B86AEWAvDk7tM8ufMki3Ep/txr8nJP4B7O+s5wVmvHE5qB9Sdg46laDo67V4JE16uIe89yfl/DhbUDLqwfMBNKUq6IqAQYarZxutPFmS4Xnc1WVislzicynEukmUnnKItS7MaIxcgpu5lTNgkS7XoV2eyioiISicvKPoQgaLBYBrHbj2O3ncBuP47B0EoqlWoARCgUoiBvmut0OgUO1YfNVrPBRFGkHC9IZ2W3pUdxp+ZBCHq1oiB0rTIgnmcHIn0QqwFiTQJEfXqrw9+Mt6sXX1cPvq5evF3dt3xWtHo1bn8zpUwv7W+lSB/UxnKr7aWmNiueNgkQVnetl16KRmtgCM6TDwal9lJ198Fmkw5SDQ5K6mFoSArmu0ErrFwps5HcIHgQZOGgpiKqi5oAHbYOZXJp0DXIoK2TpmSkrr003XgxTlBDU99VgBgDi/emvl/Vrem5Ou9hfjfFYbYuXdhlZMhfUw5DzTbanKb/lJNLr4R6xU9PCYLwMeDNwJ4oiqPX+d8F4C+Bh4Es8NM3k2f1UqGRih4Q/ePLbGdW+Fmrh+bRAIsten5D9Rf05y4xN/dmXut7GPeMiNqm42gQvnPun9lbW8Hm8TF43xs5KvSxcumQYqGMu8VC74gZX+Q5il//AoVgEADD6CjW176Gyn2neEq3yXd2nuDZ8LOki2k0gobjvuPc13If9zmH6dtfQ1h5HFa/CRn5YJGzC7peBZ33E/ed5Zk9LU8tRzm3dsDynjR1pNOoONbq4HSXk9MdLhxeE7P5AucSac4nMqzL0RtGlcBxm5mzdjNn7GZO2s0YKocyIK6QSFwilZpWVIRO14Tddhy7/Tg2+wls1lGKRYFQKNQAiVRKeoFRqVT4/f4GQLjd7oaojXLqSFEQR1spitspKTYFQCOga7aga7OibbWga7VeV0FIY6f7DQpib22ldlpUEHA1t+Dr7sXb1YOvqwdvVw960wvnGV1dlYrI4a48vVQHCOVqnDy9VJ1aqgLCaJXM3IZoDRkS+WDj3QdtIIB+eEhSEEM3v/uQK+WUYL4qHOqnl7QqrdRecg0y4BxgyD1Ev9aJObZcUw+70xBbqstdskqTdPVw8A6B1njD75UoiuynCjIcai2m+q1pg1bFgN/GcL16+E+w9/D9VrdTafwx8PtADvgqMAH8siiKn7jBx90PpIGPPw80Hka60/EwcBb4y5tJ032p0Hj8Dz9Cf2KUZxLf4E96HmTzuIOf0nye1xQ+y0LwB3lN8fXYoxqEQSNPr3+ezeAkNo+XwfveysFuC9vzSdRaFb0TLjrV62i+83lyz54DUcQwPo79zW8md8843yrO8NjmY1yMXKQiVvCZfNzXch+var6LsyUBy/rTsPKY9AMMknHd8xD0vJpMy72cixl4ejnGUysxgmGpJWXWqTnd5eJ0p4sTHU4Eu45LmRznZUhUDWu3VsNZu5nTdgkUw2YtR7lFkokrMigukcttyv8OGiyWIVlFSKDQapuv8SGi0doLntvtbgDE1T5EJV+S4LAtweFoK10L6hOQxlxbreharRIofCYETWMvXhRFUtF9IqvL7K4uKYDIyQF9gkqFu7VdAYOvqxdPZxc6w41f6OqrwX+Q20sHO2klubW6HKcAot2Ku6V2c7qSz0vTS8Fg3YLcgnLvHI1GuvswNCTHakjjrTdqLwHEcjEJDvF55mPzzMfn2UhuKFlgNp1NidUYcg0x4Oijq1RGuxeswWF3GjJ1TQF7+7WAuMnU1qNSheW9dINyCIaTxDI1Mz9gN1zjPXS4zajvqIfved1OaFwRRfGYIAhvA34I+ADwTVEUJ27ii+wEvvg80Phb4FuiKD4i/3oBeFAUxfDVf7a+Xio0vvnev6bHPMyvli7z7P33ctK5wi8UPsTC3Jt4dfINuMoWNp1LPP3MZzDZ7PSdfTOxcAfR7Rwmm47hcQP+xa+S++LnEbNZtO3t2N/yFjKvPsnXK9M8tvkYc7E5AHodvTzU/hAPucYZjiwhLD8qeRPFDKg00HYX9D5EoePVXDxq5ZnVOE8tR5ncTlCuiOg0Kk62O7m3182ZbjfYtJxLZXkqnuZ8MqMsz3Ub9ZyxmznjkCDRoauQTF7hMPEch4cXSCQuU6lI46LXUxGFgsjW1pby2NnZUU6Oms3ma3wIo7H2wiwWK1JA31ZKAUVpvzYfr3YZ0LVKKkLXakXbYkF11XRLNeI7srJMZHWJ3dVlIitLCiBUajVNbZ2KevB199LU3oFWf2sb1PlMUQHDC/kPUntJenb4TajVdcmtwZoxXZgPUlhdA3nTW2U2y6b0kAIJXW8vqhvcfagmtzZML121HBcwB2pwcA0waG2nORVDqO4+7E7DXvD6uw/1C3LGm9sbiaYLNVM6nGQunGRlP02xXDslOuCzNngPg34rDtPNjc7eqdtftxMas6IojgiC8FHgs6IoflUQhMmXARpfBP5IFMUn5V8/BvyGKIovSISXCo3pD3yOkljiJ4ebEQfU/EH5FwgvnObu0Ntp0tv5Zuhf2D/YoP/u15PPHSeyXsDWZGC4NY3zqUcoXHgWQafD9uY3o3rrG/imbZsvrn2Jqf0pAMY947ym7SFeY2qnY/syLHxZigkH6R1d72sRex5i1XKCx9fyfHtxnwvrBxRKFdQqgfFWO/f0uLmrx43OaeC5TI6n4inOJTJkZEgMmA3c67Bwt8PCXQ4zDiHD4eFzHCYucHj4HKnUjHwfQsBiGcThOCV7ESfQ6ZqJxWINkKhOM1XbTG1tbbS1tdHa2tpwUU4xqhUfQppkqrqYKotWgYOuTQLE9TapM4dxSUGsLBGRVUS1xSSoVDS1deDr7sXX3Ye/u5em9k40N3jhvbqyySP2N1PSY0t6rt+eNjv0Chiu9h/ql+MU/2F+ntLurvLxGr+/5j0MDmEYHrqp6aWj8hHLh8sNcFiIL5CRp+DUgppuR7cEh2pyq8GDvRqtsTslLWjGllHWp+p3H6qAuMndh3JFZC2aZjaUbGgx7adqXo3PppczlyTlMNxso6vJ/H2TuXSnpLqd0PgjJIWRA84ADiQQ3LCVdANofAn4w6ug8X+KonjxOn/254CfA2hvbz+5sbFx9R+5qVr65mMYv6ZjJnGJn37bq/hNze9h36wwsPrTBDQOvrTwt+icFlztP8zuqh6TTcdoSwL7lz9MeWMdbUsLtne9kytn3Xxh/3Ge3nmaklii39nPm7vexBv1fvwr35ZAcbiJ5I6fgoE3kul6A0/E3Xx7Kcp3FveVIyz9Pgv39Xq4u8eFzWvicjbPU4dpnj1Mk5Ih0WfSc4/Dwj1OC/c4LFgrUQ4PLyhKonpPXBB02GxjOByncdhPYbefpFLRs7OzowBie3ubvDyZYzQaFUC0tbURCAQaIjfKySOONpMUNpMcbcpGdbFmVDcoiFYravu1WUy5VJLIiqweZBVRNakFQYWrpRV/T58CCU9nF1rdzSeEiqJI5rBQB4g0+5uphstxdq8RT7sEh2v8Bzl7KT87Rz4YJB+cozC/QCUt3wFRqdD3dMttpZtPbgXpMFDVe1iILxA8CLJ2uEZJPvhk0piU9tKga5BB5wA9aNHvzdfgsDsNqVDtL7W3S7HzVUg0j4Ot5aZ2H6TFuCRzMiDmQlKsd3XSTqsW6PVaFTBU1cMrMbH1Tt163VYjXBAEJ5AURbEsCIIJsImiuHsTH9fJK6g99ZVf/hPGDHfxidJ3mH5Yx9vi/4Zp+ucZqgT48vLfYW3rJZt9AEHQMdKRxfO1D1PZXEM/NIT2v72b/2jZ5dPLnyWai+Iz+Xi462HeZO1lYOM8zHwektugMUjX/gbeyGbT/XxlvcLj83tc3IhTqohY9Bru7XXz4ICXwQ4H85Ui3zpI8UQ8pXgS3UY99zotipqwVXaJx58hfniew8ML5PPyxrjajN1+Aof9FA7HaazWcVKpfIOKiEQiVP+NPR5PAyTc7tqIqViuSAeDNpIUNlMcbSYpx+UXXrWALlBnVLdZrzvJVDo6Ym99hfDSIrsri4SXF0hEav+ZOAOt+GU4+Hp68XZ235IHUc1fulpBVO+ZCwI4/GY87ZI57Wm30tRmRS+H81VyOWm8dW6O/FyQ/NycdHdavr4nGI0YBgYwDA/JZ0WH0Pf13XA5ThRFwpmwohyqU0yhTO3F3mv01uDgGmTQ0UNrLoOqmrlUBUQ17VVQS2qhebymIPxjNxWtIYoie6lCAxzmwsmGW9N2o5bhZhvDAZvy3OOxoNPcUQ//Wet2Q+MeoBNQhqVFUfz4TXxcJ88PjTcB76VmhP+VKIpnbvR3vhRoPP3e/4XXGOAt96n4fcNvkr/8Y9yTPs5X1/4BvXeYbPZu2tq19F35GML0OQwjI2R/8i38b8c039h8jLJY5r6W+/ix5vu5d3cZ1eznpOtfKg30vIbK6A8zY7mXry2n+fpshCV5ymnQb+XBAS9397k5sml5MpHhW/EUCxnpHb9Pp+EBl5X7nVbudVpwEScef5aD+DPE488okNBqXZKKkJWE2TxILBZnY2NDeVQnmqojr/WtpnovopyqqogURxvJBhWhsunQd9jQtVvRtdvQtViuNaorFQ7CO+wuLxJeXmR3eYH9jTUlydXq9uDv7cPf009zbz/ert5bOhIkVkQS+7lrAFGQJ64ElYCr2Yynw1oDRGvNoC4nk1J7KTgnwSEYpLCyWtuettsl32F4WH4ekrKXbnCnolgpspZYa4DD/MG8smMjINBp71SW44ZcQ/RbWmmqZi+FJ2v+Q/XsrcZYM6er6sE7fFPTS6VyhdVohrlQUvEe5kKN5nS7y3QNIJrtd2I1/qvV7WxP/RPQA1wB5KQ3RFEU33+Dj3sEeBBoAiLAB5FyqxBF8W/kkdsPAz+ANHL7MzfyM+DFQyOfybD9P59kPx/m62/7Ni3zWh7c+lGe2H6EvLmdinAvY5o5mh79a7Q+H/mfewd/7ZnmyfBTWHVW3t7zVn5UcNA28wVpfwIBul5FZeRHuGi6jy8sZnl0LkIkWUCtEjjb5eL1wz4Gu51Mlo54PJbi2USaQkVErxK4y27hAZeVV7us9OhyHB6eVyCRza4AoNHYcDrvwum8G6fzboyGbvb29lhfX2djY4PNzU0ln8lqtdLR0UF7ezttbW14vV7U8gugWBYp7mY42kwqSqJ8IPf31QLagAV9FRAdVtT2a89PZg7jChzCy4tEVpYoZKU+vM5oxN/Th793gObeAfy9/VicNxc2BzVA7G0m2dtIsb8hQaJ6plalEXAHLA2AcLeY0ciHjUrRaIN6yAeDFLdqC2kar1cCw8iwtEU9NIy25cbjrdVwvvrluOX4MkcV6QVZr9Yr0RpVg7pP68QUXaxTD1MQW6HmP7jq1IMMCHfvTS3HpQsl5sON6mFhN6VcQNSpVfT7LRIYmm0MB+wMNt8Zbb1TUt1OaASBYfEVEof7YqHxlT/6fxk7PMa55BMU7n+Mvsn/wUbkSSJqHVrDq5lY/EfsoSuofuodfHh4m29Gn8ahd/Ce7rfyroMolqlPSblOzk7Ekz/DvPdhPrtY4j+mQkSSBYxaNQ/0e3jdsA9Xi4WnM1m+Fk2ymJVenPtMeh5y2XjAZeWMVUshfZGD2Hc4iD9DOh0ERNRqEw7HaQUSJmM/4XBEURGbm5vK8pzD4aCzs5OOjg46OjpwOmvHesrpI47kFlNhQxp7VVSEVScBoqokWizXXJUr5vNE1pYlSCwtEF5ZJBWV9kdUajVN7Z009/bLkOjHFWi96agNURRJRnMKHPY2k+xv1hJc1RoVTW3SaGv14Wo2o9aoEEWR4k6I/Nys5D/MzVGYCyopwCAtUkqTSxIkDENDaJqabvh1xXIx5g/mCR4EFZN6M7mpXI5z6B0MugZr00vOATrKoNmbrbWWdqdqJ28BHO2NcPCP31T2kiiK7Cbz16iH9brcJadJ26AchpvtdHvMaO+Y03fqeep2QuPTwPtv5DXcrnqx0PjaL/4FI7aTfNb3MdpSx3DsisxkV9Cb3syxC3+Gq0ng0Z8Z4+/yj2LSmPjvXT/Ij4VXMM18TtrYHXyY2OBP8Im9Lr4wGWY1mkGrFnig38sbx5vR+Y08nkjzaDRJtFhCLcDddgtvaLLz+iYbHnGX2MG3icW+Qzz+LJVKDkHQ4bCfkCDhuhuLeZRIJMrq6ipra2tsbW1RlG8dNDU1KYDo6OjALs/5VzerC2sJCmsJjtaT0nU5kKK/A2b0soLQtdtQOxpVRKVSJra9JbeZFthdXiS6tYEot3HsXp/UYuobwN/Tj7e756aN6qoHsbchtZb2NpINLSaVRqCpxYKnw4a3w4q3w4qz2YxaLQNie5v87KzyyM3OKQenJIO6R/If6tpMausL5x1V01vnYzVABA+C7GVr460tlhbFexhyDTHo6MWbjiFEZmrqYXe6FukiqMEzUAcH2X+4ifHWYrnC6n6GuXCiwYOI121Od7pNSmLrcEB63EltvVO3WrcTGt8EjgHn+T6+3Hfpf/wrOrWO80Of5dTC2/l25EvozG/j2HN/hXbcya8/uEOUFD/S/np+KbKNK/hl0JqonPgpnvW+m4/NHPH4/B4icFeXmzdNNGMOmPlGKsNXowky5Qo2jYqHXDbe0GTnfrsWMX1BAUU1ksNobMftfgC36wEcjjPE41nW1tZYXV1lfX1dmWzyer0NSsIiH8KRTnFmKawlKawnOFpLUE5UjVwN+k4b+k4bunbbdXcicqkkocUgoYUgoaV5IivLFAvS59SbzQogmnsH8Pf0YbI7bvp7nEkUiKwl2VtPypBIkc9IL34qtYC7RWoxeduteDtsuAJ1CqIOELmZGfJzwRogtFoMfX0YRkYk9TA8jL6//4YGdblSZj25zlxsrmEHouo/qAQV3fbuBkAMWFqxxzfr4DAl+w+yR6A1yTen69TDTW5Pp/JFKXMpVNdeiqQ4qraXNCoG/dYG/2HAb8V6p710p16GunO57xZq4dIVDP96yHJqDp2ziaWtb5DVv4bj0/9McqTEb963wZB7kA+JbgYmPwMaA0en/g8eER7m7y4m2TnM0WTR885TrfQMuHmykOPL+wkSpTJOjZo3eRz8oNfBCVOB5ME32Y8+ysHBk1QqBVQqA07n3bjd9+N23U+p5FKUxOrqqmJcOxwOuru76erqoqurqwaJskgxnJYgsZbgaCNBRY6zUFl16Lts6Lvs6LvsaLyN6a6iKHIQ2lYgsbMQJB6STHWVWo23s1tqMckqwtl84z5/tY7yJfY3UkTWJUhE1pOk5WkrQSXgbjHjkeHg7bDiDlhQa68CxMwMudnZFwDECIbRUfT9fTdckCuUCyzFlyT1EJPgsBhfVOI1dCqddPfBLasH1yB9WgfG6GINEOEp+faD/DNhcjfC4SbD+arBfFdPL20e1NpLLrOOkYCtQUF039l9uFPfxbrd01M+4LT8y/Pfq7BCeHHQ+MwHfp+79A/wrexXcRfMLB6ZGdmYIda+yB88GOM9Tad4/9Q30Baz5Cd+iv+teSd//VyKZL7EXd0uHj7ZStiu5lN7cXYKRSxqFT/QZOeHfE5O6Q9IHHyD/f1HSSQuARUMhhaaml5LU9NDWK0nCO3ssbS0xNLSEnt70rfOZDLR1dWlgMIlz/2L5QpH22kKq4cU1pIcrScR5QMzarcBfaddAYXa1diiKB4ViKwssbMQlECxOE9e3qo2WKwE+gcJDAzT0j+Er7fvpttMlXKFWCgjwWFNAkQ8XBvftHmM+Dpt+DpteDtteNosaHTqGiBFOJ8VAAAgAElEQVRmZuT20vMAYnRUgcTNACJ1lGpQDnOxOdYSa5TlO9JWrVUZbx12DzPo6KdLVKGJzNZaS+EpSNdNjVf9h+aJ2ojrTfgPxXKFlf10g3qYCyeVYD5BgE63+ZrpJa/12mGDO3Wnvpt1O5XGO4E/Ab6FFJD6KuDXRVH8zEv95C+mXgw0vv1Lf0eHuZcZYZqVnS3akxbUmq/yP38wy4dEF2/ZuEy58wEecb+PP7xQJnNU5vXDPk4e9/OtSoFvHaQQgQecVn6s2cWD1iyJ/S+yG/kP2cQGi2UIT9Pr8Hhehyi2srKywtLSEisrKxQKBVQqFR0dHfT29tLT04PX60WlUiFWRIqRLIXlQworhxTWEogF6cVP4zPJKsKGvtOO2t74Ip85jMsKYo7QQpDI2opyPMgZaCXQP0jLwDCBgSFczTfeVoaaDxGR1cPemtRqqmYxGcxavJ02fF1VSFgxWnRS2ywcJjc1TX5m+vqA6O+vKYibBEQsFyN4ECQYCyrP9dfjPEZPrb3kHmLQ3ktrLi3Ha8jqITJzlf8w2Lgg5x8D443bcNXluNlQkpmdBHPhJIu7aY7kJUy9RsVgvffQbGXAb8NyJ9b7Tr0C6nZCYxJ4XVVdCILgAb5xMzEi3416MdAI/up/kC4mWUxdolAaoS3yt/zf78zz+9kCr0mneW7g13jv/AiR1BGvG/YxdNzH57JplrMFmvVa3uV38cNNKgzJb7Ab+XcSCenz22zH8XkfpqnptRweapifn2dpaYlwWJoZsFqt9PX10dfXR1dXFwaDQTKuD/Lkq5BYSVCR+/6aJiP6Hrt0Orbb0RDBIYoi8XCI7eA0O8FZdhaDyuKcWqvF39NHYGCYQP8Qgf5BTLYbB+KBlMdUbS9VW03VZTm1VoWnzSrBocuKr9OOrUlSN6V4XGovTU+Tn5omNzNDuRpq+CIBsZfdIxgLMhebY+5gjmAsSCRbu4HRZm2rmdOuQYZsnTQl9yB8pbYDEZmr7T9oTVKkRv2CnHcYtDfOrIpnjiQ4hBLMhpLMhhKsRWvqqtpeqqqHkYCNTved9tKdeuXW7YTGtCiKY3W/VgGT9b93O+tWofG5v/oIZ0KjXEk8w2pOx4nlr/I779zmt0spXi1a+HXd7/BvOzaOtTk4drqZzxWz7B2VGLcY+fm2Ju7RzLEXfoRo9DFEsYTZ3IfP9xa8njcRjQoEg0GCwSCJRAJBEGhra1NA4fP5EASBSrZIfumQ/FKcwvIhZTniQmXTYehxoO9xoO91oHHUlETVj9iem2Zrbobt4AyZuHRn22R3EOgfomVgiMDAMN6unps6P1oqlolupSVAyIZ1ohouKIDTb8bXacXXZcfXacPVIk0yVXI58nNzDYAobm7KHyeg6+7GODaGYXwM49gY+oGBFwSEKIrsZnYVMMzF5ggeBInm5HgReUFu2D3MkGtIajGZAlgP1iTlEJ6UILG/AHJLCoNDai01j0PzsVv2H6rqYTaUZC6UIJSo5VS1OIyMBGyMBOzSc8ud6aU79f1XLxc0bkY3f1UQhK8Bj8i//lHgKy/1E9+u0gVTYIcdfZi+5SIffXCLn65kOCUEeODg/aQ1Lt7xug6+aSzzbCbJXXYzf9nnoDP7JcKr/8JsfhOt1kVb63vw+X6IWMzIzPQM8/OfJpPJoFar6enp4cEHH2RgYACTySS1nEJpUo9vkV+Mc7SZBBEEgwZ9jx3rA63oexxoPLVzlaIoEt3aYHtuhq25abaDM2QThwBYnC7ahsdoGx6jdXgUZ3PLTb1gZRIFdlcThFcS7K4k2N9MUZFTSs0OPb5OG0P3NuPrsuNtt6IzahBLJQpLS+SefYq96WlyU9MUlpeVJFdNczPGsTGc73wHhtExDKMjqGXT/noliiLb6W2lvTQXk0BRPRBUnWC6J3CPAolBfZO0IBeegtnHIfznEF+r/aUWvwSIwTfJoJgAe9sN/YdKRWQtlpGUw05NQcTr/IfuJjOnu1wKJIabbTjNd5Jb79SdqtbNGuFvB+5D8jS+I4ri57/bX9jz1a0qjfPv/wQ2rZPHw7OkNR8nd9cRv5gy8rr4b9HZ1U562MFM6Yhxq5FfbdHSnvhHdnc/TaVSwOE4S0vgXcAJZmbmmZ6eJpFIoNVq6e/vZ2hoiL6+PvR6PZV8ifxCnPzCAfnFOJW09EKkbbVg6HdiGHCha7Mq001VSGzNTrMdnGZ7bkaJAre4myRADI3SNjKGw9d8Q0hUKiIHoYwMiUN2VxIko9K7ZbVGhbfTir/Ljr/bjrfThsWpl4zqzU1y0zPkp6ek57k55dSoym6XFMTYKMaxcYxjo2g8nuf9GqqAmI3NMhedU9pMKfkanEbQ0OfsY8g9JCkI1xB9ajPG/QVJPVRVRH1An6OjBoaqSW313fDf/ahUYTGSYlZpL0mLcll5qECnVjHgt8pwkLanh5qtmHR3/Ic79Z+zvuvtKUEQegGfKIpPXfX79wM7oiiuvNRP/mLqVqCxvbZO8SMrbGVWSS/8B//4I8v8ZazMW1O/g2Ogj+l2PW6Dlt9uNzCW/Ah7e/8BqGj2vw2v98dZXs5w+fJldnd3EQSBnp4exsfHGRgYQK/XU04WyM0dkJuNUlhNQFlEZdKg73NiGHBi6HOittbepaYOomxOT7IxdZmN6SuKkrB5vAokWofHsHt9N4TEUb5EZC0pqYjVBJHVBEdy7IbRpqO5RwJEc48dT5sVtVZFKR4nd+UKuakp8tMz5KenKctGtWAwYBgeliExhnF8DG1b2/N+HdWQvtnYLLPRWeZic8zGZpUdCK1KS7+zX1IP7iGGnUP0iRp0e7ONgMhJLTcElRTQV51gqhrVN7EglymUCIZr7aXZUJKlvZRy+8GsU0uqQQbESMBOn89yZ3v6Tv2XqtsBjS8Cvy2K4tRVv38K+KAoim95qZ/8xdStQOOfP/BB7te/lqdTj/Flz2f4Tf0B70/+LonBCTbaDLzLb+U96s8RD/0vBEFFS8u70evexJUrG8zMzFAsFmlubmZiYoLR0VEsFgvFaI7cTJT8XIyjTfkdtNuAYaQJ44i7QU0c5XNszU6zOX2FjekrxLYlH8Bos9MxdoyOsWO0jYxj977wO+fqRJPSalpNENtOS6asAO6AGX+Pg+ZuG/4eB7YmA1QqFJZXJEhcvkzuyhXpHjWAWo2+rw/j2KgMiHH0vb0Imuu/yxZFkb3sngQI+TEXnVNaTFUFMdI0woh7hBHXEL0VAe3urGRShyelR3WCSaUF33AdICakhTndjc+yHmSOmA0lmNmRWktzoSRrdemtbrOOkRa7oiBGAnY6XHfuTt+pO3U7PI3Oq4EBIIric3J67Su+fAUPFV2FWGmWh61xPhJ7D5sdw+Q7jHzIF2Jw/2c5KCVo9v8wGs0P8+wz86yu/htarZaxsTFOnTpFIBCglCiQu7RPZHKJ4o6UXKttsWB7fQfGEbe0VCcIiKJIbHuT1UsXWLv8HKHFIJVyGY1WR8vQCCMPvIaO8eN42jtfcPxVFEUOI1lCS4fsLB4SWjpU7kNo9Wp8XTZOPtxJc7cdX7cdvVFDOZUiNzlF7l8us3XlCrnJSeUmhNrlwnjsGPYffjumY8cwjI6iMj7/BnM8H2c6Os1stAaJqkmtFtT0OHp4sO1BBRB9FRX6vTkIXYH5j0kqQm5JodZLCa5j74DAMQkQnqEbHggSRZFQIt9gTs+GkoTrDOpWp2RQ/9DxFgUQPtud/Yc7dae+m/VC0HihucRbO8T8PSqvPkCsEGGyf5L7Ds/wVd/rKQ/Z+CPzI3jCn8HiOIvR+P+3d+bxWVXX3v+uzPOckJGQMGcOgQQQUBEQtYpWW2mtWm2vr61a7dvh7b32eltv23vt+Hawtdqi1nqt1VZB64AVRZQpISQkGIYEAmQeyEASMu/7xzkJMTwJUXky4Pp+Ps/nOcM++yw2J+f37L32XuuLvLutnKqqV/Dz82PVqlVkZWXh6erB6cJ66l7aR3d5CxjLPxF4VSLeqWGDM516ursoL9hDWX4uR/fm0lpvLd4Lj08g61PXEZ+aQczcpFEzz1nTaTuoOtw0KBIdrVbYCp8AD6LnBBE9K4jImYGERvsiLkJ3eTmn977DyWetnkRXaakVI8vFBc/Zswn41FX4ZGbinZGB+/TpI75Iu/q6OHDyAEX1Rexr2EdRfdHgOghBPuCkTg6Zz9x+V7zrSiyBOPi4tVCu205Y5OZlDSml32jNYIrOsNZEuI4+s8vKHtc+xP9gfQ8skHMRmBnuR05CyOAMpqToAE0tqigTwGjDU88AW4wxjw07/iVgjTHmxnGw7yzGOjz1yuNPkXZwBvtb9uAV9wh39f2E9qXR3O/+Y2aZ94mI+Ar5e/woLT1CUFAQy5cvJy0tDVPbSfvuGjoK6zFdfbiFe+OTEYFPejhuYZZWdrQ0U5q7k7I9uzhevI/e7i7cPD2JT80gMXMRCZkL8Q8dObKq6TecrG63BOJQE1WlzYNrI3yDPImeHUTMnCBi5gQTGOGNOX2a00XFHxhq6mu2/CEu/v54Z2TgnZlh9SLS0kaczWSM4VjrMYoaithXv4+ihiIONh2kt99aEBjhE0FaWBqp4amkhqaS5OaLb20JVOZbn+pCK7852DkgUu3egy0QYXPBdXRHcldvH4dr24b4H1ooqT7FaTsB1UD8pQHndHJ0APMjA/D2OHfocEVRRmY8fBrTgBeAbmAgBetCwAO4biyZ+5zBWEXjb1/9ATkBF7O5cyNb/CJ4O/sS/tX/ITI9m2lpuZndu4/h6enJihUrWJS1kJ73mzn1biU9lW2IuwveqWH4ZkfiER+AiNDe3MThXds5tOs9Kt4vxph+AiOmkZC5iMQFi4hLSh2xNzEw3FRxoImKA01UHW4eDOTnF+JJzOxgoudYQhEQ5k3/qVN05OdzOi+Pjtw8Tu/fD73Wi90jMfGMSGRm4pGYOOJQ18Aw04BAFDcUDzqqvd28SQlLITUslbSwNFJ8opjWdAIq99giseeMk9rV03JMRy+A6ExriClszjkFos2Rg7r2FL12TnF/TzfmD/E9JEcHMCtCHdSK4gyc7tMwxtQCS0XkUmAg894/jDFbPu5Nx4NIlxg6+zro8yzhrTnXcXPAM6S6NpGfv5qGhnKys7O5+KIV9Be10PCLAvqau3CL8CZo3Ux8MiJw8XajvbmJ/a+9zOFd71FxYD8YQ3B0LDnXfYbZORcRHp8w4rDP6VPdVBxo4kTJSU6UnBwM5ucf6sWMtFCiZwcPikTvyZN05OXR8Vgejbl5dB04YA01ubvjnZpK6G234bMwC+/0dFyDHIe76OrroqSxhOKG4rOGmVzEhVlBs1gdv5rUsFRSA2cys70F1+oCKNsD72yAloHFei6Wz2HelRCTZQnFtORzDjE1tnV9YAW1lf/hjIM6zM+T5OgALp0bPigQ09VBrShTjjGt05hMjKWncaqpidof7aa+s5o7YgOZl13JV3iGnTuW4esbzbqr1xHe4EXLP4/R39qNx4wA/C+OxWtuCH19vRzZs4v9W9/kaMEeTH8/YXHxzM65iDmLLyI01rF/oLenj+rSlkGRaDhhjfN7+rgRMzeYuPkhxM0PJjDch57aWjpy8+jIy6UjN4/uMmv2snh54Z2Rgc/ChfgsWoR3eprD8N/GGCpOVVBQX+BwmGmazzRLHMJTSQ2eT3Kvwad2P1TttXoQ9QcZjOQaFG+JQ8wC6zsyDTxHX6xX2Xx62AK5Vmpazzio40K8SY46s3o6JTqQiIBzh+5QFMV5jOeK8CnHCz/8GSvdLqemrxJJjuY28yS7dl1MfHwan8q4jNMvVtJU14HHdH8CPzcPz4RAGiuOs/2J5zjw7tt0trfhFxLKoqs/TdKKlYTGTnd4n7amTo4VN1Je1EjFgZP0dvfj4ipEJgaSc00icfNDCI/3p7+5iY6dO2n/1Q7qd+4aTEXq4uuLd9YCAq9dh8/ChXgnJyMOhrh6+nooOVnC3rq9FNQVsLduL42djQD4uPmQHJbMLUm3kBaaQqqrPxGNR6EqH3b82XJUD+SC8AmzhCH505ZIRC8A39AR23FAIIoqWiiqtD7FlWdWULsIzIrwY8nM0EHndHJUIIE+mv9BUS5ULkjRiGgPhUAoCWzhX3we5lBRJjNnLGKlpHHqqcO4hXkTctN8PJOCOJKfS8GfX+Z4cSGu7u7Mzl5K8sWXMT01HZdhcYtMv6G2vJXyfQ2UFzfSWGH1JvxDvJi3JIr4lFCiZwfh1t9NR14e7X/9K+U7dljDTVhOa5/sbEK+cBPeCxfiNW8e4nq2g7elq4XC+sJBgShuKB7MCxHjF8OS6CVkRmSS7hfPrNZ6XCvzoHgLVP38zFoIDz/LQZ1z55mexCihNowxVDSdprjSsUC4uQhzpvmzJimSlNhAUqIDmKcOakX5xHFhioZHNM3dDRSsCeGKY26I12KWlk2ns6MR/5Vx+F0Sw6Hd77Hzm3/hZFUF/qHhLFt/C6mXXX5WdNj+vn6qDjdTtreeIwX1dLR0Iy5C1MxAllw3k/jUUILDPeksKqZ925tUP7SDjsJC6OlB3N3xXrCA8Pvuw3fpErySks5aQDcQemNv3d7BnkRpcylgrYmYFzKPG+bcQGZ4OhkuvkTUH4YTu2Hvf8NJe1G+i/uZtRADAhE2Z8RgfR9GIFJjA0mNCWRupD9e7ioQivJJ54Lzaex6eSOR2wIpO/U+dWufp+7w1VzVlIFPgB8hN82j/HgB7/31aZqqKgiLi2fx9euZnb0UlyG/+Pt6+6k40ETZ3jqOFjbQ2daDm7sL01NCmZkZTnxKKK4dLbRte5e2d7bS/t52+ltbQQSvpCR8lyzGZ8kSfBYsOGsRXb/pp6y5jNyaXPJq89hbt3dw4Zyfux/p4elkRmSSGTSHlM7T+FQVQsVuqMg704vwDYe4HIjLhthsa7rrCOlGzzXENCAQqTGBKhCKcgGjPo0ROPpqPjH+q6hyqaS+bAGXNyfjFxaIrA3gxcd+SEVJMWHTZ3D1//1XZi9aMjhd1RhDXfkpDuys5nBeLV3tvbh7uTIjNYyZmeHEzQ+m79D7tG19jqofv0NncTEAruFh+K9ehd/y5fjk5OAW/MFYScNFIq8mbzD8RqRvJDlROWSGZ5DhGc6s5mpcK3LhvSeh7n2s0LguEJFs9SLisq1PcMKIw0zNHd0UVrRQeKLZ+lQ009Bm+TSGDzGlqUAoivIhcapoiMha4JeAK/AHY8x/Dzv/RaysgJX2od8YY/7wce4ZRQy9/T3UxR8lvflaQgJDOB59lHcf/BMePr6svuNuUi5dPeivaG/p4sCOag7urKGppgNXdxcS08OYkx1JzCx/ugvzOfXy3zh235v01tWBiwve6emE33cvfitW4Dlv3gfWSYwmElG+USyPXc7CiEwW4U1M7UGkIhd2/BU6LMc2noEQuxCS1lkCEZMFXgEO/62dPX2UVLdSMCgQVqIgq21hVrgfl8yNID02kLTYIBUIRVE+Nk4TDRFxBR4GVgMVQK6IbDLGvD+s6LPGmLvP130jvKKo76wmqDubuW6x7Gx7hbK/7WbOkuWs+vJX8fbztyK0ljZTtLWSsvw6+vsMUbMCufTmeSQkBdC7dzennvkfjm7ZQl9LC+Llhd/y5fivXoXv8uVn9Saq26rZUb2DHVU72FW96yyRWBSewSLjQUztQSh7F7ZugJ4O6+LQWTBnrd2LyLFWVTtYrNffbzjS0D7Yeyg40UxJdetgJNcIf08y4oL4zMJYMmKDSIkNJMBLZzEpinJ+cWZPIxsoNcYcARCRvwDrgOGicd7Y8O//zhr3NZR1lHBRWyZ53a9zrLaIy++8l+RLVgFQXtRA7j/KqStvxcPbjdSLY0leHoXHsWJaNv6G41/bTH97Oy7+/vivvBS/VavwW7bsA76J9p52cmty2VG1g+1V2ylvLQcgzDuMZTHLyA5PZ1GfKzG1B+DwdnjrMTsFqVjpRzNvhhkXwfSl4Oc4P0XdqU4KjlsCUXiihcKKZk51WuswfD1cSYsN4kvLEsmICyQjLpjIQF0HoSiK83GmaMQAJ4bsVwA5Dspdb+foOAR83RhzYngBEbkDuANg+nTHayYAwhv8rSx9PjUEmiMcr9/Pp//t+8TOT6G8qJHcl49Sf/wUAWFeXPz5uSREdtH+0os0fO4lemtqcPH1xf/yywm44gp8c7IH10wYYyhrLmNrxVbeqXiHwrpCek0vXq5eZEVmccOsa1kqvsyqOYQcfAfe+j3094K4WiE3sv8FZiyD6Ysd5ofo6u2juLKV/GNN5B9vovBE82C6UVcXYV6kP9ekR5MeF0RGXBAzw/1w1ZXUiqJMAM4UDUdvteFTtV4CnjHGdInIncCTwMqzLjLmUeBRsGZPjXTDae7RtPW0kuySwe7y51n3rfvxC0nkpV8VcKKkiYBwb1Z+YQ5R7SW0PvEAx7dvB1dX/JYtI+Bb38R/5crBHkV3Xzd5ldvZWrGVrRVbqWyz3C5zg+dyS9LNLPWaRsbJajzL34Wd90PvaUskYrJg6dcg/iKYngOe/mfZ2djWxZ5jTYOffZUtdPf2A9Zq6qwZIdweG0jm9CCSogJ1LYSiKJMGZ4pGBRA3ZD8WqBpawBjTOGT3MeChj3qzwt07CfeK4kT7EQ60vMuKm26j9WQUmzfsxs3DlWXXJxBbv4umB75LdVUVblFRhN/7NQKvvx73iAgAOno6eKf8NTaXb+a9yvfo6O3A09WTxVGLuX3W9aw43U3k8V3w5q/gtOW3IHw+ZN0KiZdYQjHMad3fbyitb2PPsSbyyq2exICz2sPVhZSYAG5dEk9WfDAL4oOJ8NdhJkVRJi/OFI1cYLaIJGDNjloPfH5oARGJMsZU27vXACUf9WaFT21ipe8VVFNJ1MIUqo8lcLy4lIT0UDLc99H+4Hepq6/HOyODaff/G34XX4y4udHR08GbR19j87HNbKvYRmdfJ6FeoVyVcAWXeEWxqLES78NbYNtT1o38o2DulZZIJKwA/8gP2NHd209hRTO7j54kt/wk+ceaaLV9EaG+HiyID2b9ojiy4oNJiQnU2UyKokwpnCYaxpheEbkbeB1ryu0GY8x+EXkQyDPGbAK+JiLXAL3ASeCLH/V+MX3R9Jt+ar0bCW9dSXNdE9lZQtDz36bl2HF8Fi8m+ic/wScnG4Nhd00ufz/8d7Yc30JnXydh3mFcm3gVa1wCWHCiGNd3NkBnizXkFJcDl/0HzF5tObKHrJHo6u2j4Hgzu46eZOeRRvKPN9HZYw01zZnmx1VpUWTFh5AVH8yMUB/NKqcoypTmglkRXvT1v9Nn+ij27eFUcxSLPXPxeuVxPBISmHb//fgtu4jqtmpeLHuRjaUbqWyrxN/DnyvjVrIWPzKPF+BatsWa5eQTak2Dnb0aEi8F7zPhyDt7+th7vJldRxvZeaSRvceb6ertRwTmRwawODGUnMQQsmeEEOyrmeUURZkc6IrwITz10A+51HMF77fm09KZSnrdRrwOvEHYXXcR9n/uoORUKU9s/Tabj22m3/SzODKbe8MWs/JEEZ5v/hZMHwTEwsLbYP7VELd4MMFQX7+h+EQz2w7Xs+1wA3tPNNPd24+LQFJ0ADcvjicnMZTsGSEa3VVRlAueC0I0fMr7IRAqPCqZcewkEQ17iHn8cQ4nePCdt77C7prd+Lr7cnPMSta3tBCz5zXoPgUBMbD0Hmv1dXTm4LBTdctpth2q5p3D9bxX2jAYpyk52nJaL04MZeGMEAK9VSQURflkcUGIRqRrLJ19HXQ0hTGr4RW8H/0Z3615hn+++k/CvEL5xrQVXH8kH/9Df7RChietg/T1EL8MXFzo7esn98hJ3iypZeuheg7XWSHPI/w9WTlvGivmhLFsVhihfp4T/C9VFEWZWKa8aNScOE6EtxU6ZPGhtyj9jxt4MP8eDIa7AtO45eC7+JzeC9NS4ZpfQ8r14OFLe1cv296vZfP7tWw5UEdzRw8ebi7kJITw2YVxLJ8Txtxp/uq4VhRFGcKUF41//PRhLvf+FDV9ldSvC+LXtb9nkXc0Pzh2gOj2gzD3KmsIavpiOnv7ebOkjo0FJbx9qJ7u3n6CfNxZOTeCNcnTWD47HF/PKd8kiqIoTmPKvyFjuiPBG6q8angksoh7ur348tGduMxaBZc9QP+0NLaXNfLCc/t4fX8NbV29RPh7clPOdNYkRbJoRjBurmcHCFQURVHOZsqLxkCWvo0xb/HtplZuNv3w2adombGW5/MreerPb1Pe2IG/pxtXpkZybUYMOYmhGrtJURTlIzClRWPjhsfI8JpN2an3WebRxs3B2TSufZjf7Wzk6We2cLqnj6z4YL6+eg6XJ0fq6mtFUZSPyZQWjdN5FbgGzKPKpZJvBi/iN9Me5Le/2ktnTx/XZsRw+7IEUmICz12RoiiKMiamtGhEiZWlrye4gC803Et+8RGuTI3kG2vmMjPcb6LNUxRFueCY0qJhZemr4UXPq6hsEx75QhZrUyLPfaGiKIrykZiy04Ye+da38HcPorangq7QFF69d4UKhqIoipOZsqIR0xYGwHHvGp7+cg7h/rpaW1EUxdlMWdGY5h5DW08rCdfdpuE9FEVRxokpKRrb//kPwr2iqOusYu2ylIk2R1EU5RPDlBSN0o3v4e7iQTWVGhtKURRlHJmSojGQpa8zUUOTK4qijCdTUjQiPKM52VXHrd+4f6JNURRF+UQx5USjvqqSYM9w6rqrJtoURVGUTxxTTjTcei2TK90rJ9gSRVGUTx5TTjTccaer7zQ5t9440aYoiqJ84nCqaIjIWhE5KCKlIvIdB+c9ReRZ+/wuEZlxrjrdXTyo66wiaUGWM0xWFEVRRsFpoiEirsDDwBVAEvA5EUkaVuxLQJMxZhbwC+Chc9frQk2fDk0piqJMBM7saWQDpcaYI8aYbuAvwLphZdYBT9rbzwOXyRgWXtQEt0MbzSEAAAsPSURBVJ5XQxVFUZSx4UzRiAFODNmvsI85LGOM6QVagNDhFYnIHSKSJyJ53X2dfOWH5+yQKIqiKE7AmaLhqMdgPkIZjDGPGmMWGmMW+k0POy/GKYqiKB8eZ4pGBRA3ZD8WGL64YrCMiLgBgcBJJ9qkKIqifAycKRq5wGwRSRARD2A9sGlYmU3Arfb2DcAWY8xZPQ1FURRlcuC0zH3GmF4RuRt4HXAFNhhj9ovIg0CeMWYT8EfgKREpxephrHeWPYqiKMrHx6npXo0xrwCvDDv2wJDtTuAzzrRBURRFOX9MuRXhiqIoysShoqEoiqKMGRUNRVEUZcyoaCiKoihjRqbaDFcROQUcnGg7xkAY0DDRRowBtfP8MhXsnAo2gtp5vplrjPH/uJU4dfaUkzhojFk40UacCxHJUzvPH2rn+WMq2Ahq5/lGRPLORz06PKUoiqKMGRUNRVEUZcxMRdF4dKINGCNq5/lF7Tx/TAUbQe0835wXO6ecI1xRFEWZOKZiT0NRFEWZIFQ0FEVRlDEzaUVDRNaKyEERKRWR7zg47ykiz9rnd4nIjAmwMU5E3hKREhHZLyL3OihziYi0iEiB/XnAUV3jYGu5iBTZNpw19U4sfmW35z4RWTABNs4d0k4FItIqIvcNKzMh7SkiG0SkTkSKhxwLEZE3ROSw/R08wrW32mUOi8itjso40cafiMgB+//0BREJGuHaUZ+PcbDzeyJSOeT/9coRrh31vTAOdj47xMZyESkY4drxbE+H7yGnPZ/GmEn3wQqlXgYkAh5AIZA0rMxXgUfs7fXAsxNgZxSwwN72Bw45sPMS4OVJ0KblQNgo568EXsXKprgY2DUJnoEaIH4ytCewAlgAFA859mPgO/b2d4CHHFwXAhyxv4Pt7eBxtHEN4GZvP+TIxrE8H+Ng5/eAb47hmRj1veBsO4ed/xnwwCRoT4fvIWc9n5O1p5ENlBpjjhhjuoG/AOuGlVkHPGlvPw9cJiKO0sc6DWNMtTEm394+BZRwdh70qcI64E/GYicQJCJRE2jPZUCZMebYBNowiDHmHc7OKjn0GXwSuNbBpZcDbxhjThpjmoA3gLXjZaMxZrMxptfe3YmVQXNCGaEtx8JY3gvnjdHstN81nwWecdb9x8oo7yGnPJ+TVTRigBND9is4+2U8WMb+o2gBQsfFOgfYw2OZwC4Hp5eISKGIvCoiyeNq2BkMsFlE9ojIHQ7Oj6XNx5P1jPwHORnaE2CaMaYarD9cIMJBmcnUrrdj9SYdca7nYzy42x5G2zDCUMpkasvlQK0x5vAI5yekPYe9h5zyfE5W0XDUYxg+N3gsZcYFEfED/gbcZ4xpHXY6H2uIJR34NfDieNtnc5ExZgFwBXCXiKwYdn4ytacHcA3wnIPTk6U9x8qkaFcRuR/oBZ4eoci5ng9n8ztgJpABVGMN/QxnUrSlzecYvZcx7u15jvfQiJc5ODZqm05W0agA4obsxwJVI5URETcgkI/W5f1YiIg71n/U08aYvw8/b4xpNca02duvAO4iEjbOZmKMqbK/64AXsLr6QxlLm48XVwD5xpja4ScmS3va1A4M4dnfdQ7KTHi72s7NTwE3GXsgezhjeD6cijGm1hjTZ4zpBx4b4f4T3pYw+L75NPDsSGXGuz1HeA855fmcrKKRC8wWkQT7V+d6YNOwMpuAAU//DcCWkf4gnIU9rvlHoMQY8/MRykQO+FpEJBurzRvHz0oQEV8R8R/YxnKOFg8rtgm4RSwWAy0DXdsJYMRfcZOhPYcw9Bm8FdjooMzrwBoRCbaHXNbYx8YFEVkL/D/gGmNMxwhlxvJ8OJVh/rPrRrj/WN4L48Eq4IAxpsLRyfFuz1HeQ855PsfDu/8RZwRciTULoAy43z72INbDD+CFNXxRCuwGEifAxmVYXbl9QIH9uRK4E7jTLnM3sB9rpsdOYOkE2Jlo37/QtmWgPYfaKcDDdnsXAQsn6P/dB0sEAoccm/D2xBKxaqAH69fZl7B8aG8Ch+3vELvsQuAPQ6693X5OS4HbxtnGUqwx64Hnc2DGYTTwymjPxzjb+ZT93O3DetlFDbfT3j/rvTCedtrHnxh4HoeUncj2HOk95JTnU8OIKIqiKGNmsg5PKYqiKJMQFQ1FURRlzKhoKIqiKGNGRUNRFEUZMyoaiqIoyphR0VA+NiJiROSpIftuIlIvIi9/yHou+TDXiEjGSNFQpzJ2xNdvTqY67aitY1pE6Qz7lcmDioZyPmgHUkTE295fDVR+mArsVbYflgys+ejOqPsjM973U5TxREVDOV+8Clxlb39gRbeIZIvIdhHZa3/PtY9/UUSeE5GXgM1DKxORRXb5RHuF7QYRybWPrbNXBD8I3ChWzoIbh11/Vt0i8i27jn0i8n37mK+I/MMOgFg8UI+IXGbfq8i+t6d9fPAXt4gsFJG37e3vicijIrIZ+JOIuIrIT+3r94nIPXa5LBHZKlYgu9flHJGERWSmiLxml98mIvNEJNC2w8Uu4yMiJ0TE3VH5c9T/hIj8Tqx8DEdE5GL731siIk+Mcp2LbUPQkGOlIjJttPspUx8VDeV88RdgvYh4AWl8MNrvAWCFMSYTeAD40ZBzS4BbjTErBw6IyFLgEWCdMeYIcD9WmJhFwKXATwB3u65njTEZxhhHcYAG6xaRNcBsrBhAGUCWWEHk1gJVxph0Y0wK8Jr9b3gCuNEYkwq4AV8ZQxtk2TZ/HrgDSAAyjTFpwNNixQf6NXCDMSYL2AD88Bx1PgrcY5f/JvBbY0wL1mrji+0yVwOvG2N6HJUfg93BwErg68BLwC+AZCBVRDIcXWCsGFEbsUJ+ICI5QLlxEC9MubDQbrRyXjDG7BMrLPPngFeGnQ4EnhSR2VjhDtyHnHvDGDM00OR8rBffGmMHfcOKh3PNkHFyL2D6GMwaWvca+7PX3vfDEpFtwE9F5CGs5E7bRCQdOGqMOWSXfRK4C/j/57jfJmPMaXt7FVbIjl4AY8xJEUkBUoA3rHBBuGKFqXCIWFFLlwLPyZlUMZ7297PAjcBbWDGYfnuO8qPxkjHGiEgRVrjvIvv++4EZWGEpHPEslnA/btswYgA/5cJBRUM5n2wCfoqVXW9obpP/BN4yxlxnC8vbQ861D6ujGksUMjkTbVOA640xB4cWtH/djsbQugX4L2PM74cXEpEsLN/If9nDS6MFwevlTA/d6xz3cxTOf78xZsk57B7ABWg2xjj6tb/JtjcEq4ezBfAdpfxodNnf/UO2B/ZHe0fsAGaJSDhWgp8ffMj7KlMQHZ5SzicbgAcHfqkOIZAzjvEvnqOOZizfyI9E5BL72OvAPSKD0W0z7eOnsNJbjoXXgdvtX+OISIyIRIhINNBhjPkzluAtwBpOmyEis+xrbwa22tvlWC9pgOtHud9m4M4Bp7j9cj8IhIvIEvuYu4ySRMpYORGOishn7PJi94IwVnj43cAvsXpIfaOVdwbGClz3AvBzrAirExVtWBlHVDSU84YxpsIY80sHp36M9av4PawhmXPVU4s1Tv+w3Zv4T6whrX0iUmzvgzU0k+TIEe6gzs3A/wA77GGY57EEJxXYLSIFWL6THxhjOoHbsIZ5irB+cT9iV/V94Jcisg3oG+WWfwCO2zYXAp83VorSG4CH7GMFWMNJo3ET8CW7/H4+mN70WeALfHBYaLTyH5d9IlJhfwZCcDuyQbmA0Si3iqIoypjRnoaiKIoyZlQ0FEVRlDGjoqEoiqKMGRUNRVEUZcyoaCiKoihjRkVDURRFGTMqGoqiKMqY+V9aEJ8DMOMmZAAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot the consumption function at various levels of persistent income pLvl\n",
+ "print('Consumption function by persistent income level pLvl for a consumer with AR1 coefficient of ' + str(PersistentExample.PrstIncCorr) + ':')\n",
+ "pLvlGrid = PersistentExample.pLvlGrid[0]\n",
+ "mLvlGrid = np.linspace(0,20,300)\n",
+ "for p in pLvlGrid:\n",
+ " M_temp = mLvlGrid + PersistentExample.solution[0].mLvlMin(p)\n",
+ " C = PersistentExample.solution[0].cFunc(M_temp,p*np.ones_like(M_temp))\n",
+ " plt.plot(M_temp,C)\n",
+ "plt.xlim(0.,20.)\n",
+ "plt.xlabel('Market resource level mLvl')\n",
+ "plt.ylabel('Consumption level cLvl')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot the value function at various persistent income levels\n",
+ "if PersistentExample.vFuncBool:\n",
+ " pGrid = PersistentExample.pLvlGrid[0]\n",
+ " M = np.linspace(0.001,5,300)\n",
+ " for p in pGrid:\n",
+ " M_temp = M+PersistentExample.solution[0].mLvlMin(p)\n",
+ " C = PersistentExample.solution[0].vFunc(M_temp,p*np.ones_like(M_temp))\n",
+ " plt.plot(M_temp,C)\n",
+ " plt.ylim([-200,0])\n",
+ " plt.xlabel('Market resource level mLvl')\n",
+ " plt.ylabel('Value v')\n",
+ " plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Simulate some data\n",
+ "PersistentExample.T_sim = 500\n",
+ "PersistentExample.track_vars = ['mLvlNow','cLvlNow','pLvlNow']\n",
+ "PersistentExample.initializeSim()\n",
+ "PersistentExample.simulate()\n",
+ "plt.plot(np.mean(PersistentExample.mLvlNow_hist,axis=1))\n",
+ "plt.xlabel('Simulated time period')\n",
+ "plt.ylabel('Average market resources mLvl')\n",
+ "plt.show()"
+ ]
+ }
+ ],
+ "metadata": {
+ "jupytext": {
+ "cell_metadata_filter": "collapsed",
+ "formats": "ipynb,py",
+ "notebook_metadata_filter": "all"
+ },
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.9"
+ },
+ "latex_envs": {
+ "LaTeX_envs_menu_present": true,
+ "autoclose": false,
+ "autocomplete": true,
+ "bibliofile": "biblio.bib",
+ "cite_by": "apalike",
+ "current_citInitial": 1,
+ "eqLabelWithNumbers": true,
+ "eqNumInitial": 1,
+ "hotkeys": {
+ "equation": "Ctrl-E",
+ "itemize": "Ctrl-I"
+ },
+ "labels_anchors": false,
+ "latex_user_defs": false,
+ "report_style_numbering": false,
+ "user_envs_cfg": false
+ },
+ "toc": {
+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": false,
+ "toc_position": {},
+ "toc_section_display": true,
+ "toc_window_display": false
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}