A string is a valid parentheses string (denoted VPS) if and only if it consists of "(" and ")" characters only, and:
<li>It is the empty string, or</li>
<li>It can be written as <code>AB</code> (<code>A</code> concatenated with <code>B</code>), where <code>A</code> and <code>B</code> are VPS's, or</li>
<li>It can be written as <code>(A)</code>, where <code>A</code> is a VPS.</li>
We can similarly define the nesting depth depth(S) of any VPS S as follows:
<li><code>depth("") = 0</code></li>
<li><code>depth(A + B) = max(depth(A), depth(B))</code>, where <code>A</code> and <code>B</code> are VPS's</li>
<li><code>depth("(" + A + ")") = 1 + depth(A)</code>, where <code>A</code> is a VPS.</li>
For example, "", "()()", and "()(()())" are VPS's (with nesting depths 0, 1, and 2), and ")(" and "(()" are not VPS's.
Given a VPS seq, split it into two disjoint subsequences A and B, such that A and B are VPS's (and A.length + B.length = seq.length).
Now choose any such A and B such that max(depth(A), depth(B)) is the minimum possible value.
Return an answer array (of length seq.length) that encodes such a choice of A and B: answer[i] = 0 if seq[i] is part of A, else answer[i] = 1. Note that even though multiple answers may exist, you may return any of them.
Example 1:
Input: seq = "(()())" Output: [0,1,1,1,1,0]
Example 2:
Input: seq = "()(())()" Output: [0,0,0,1,1,0,1,1]
Constraints:
1 <= seq.size <= 10000