1111\. Maximum Nesting Depth of Two Valid Parentheses Strings

Medium

A string is a _valid parentheses string_ (denoted VPS) if and only if it consists of `"("` and `")"` characters only, and:

*   It is the empty string, or
*   It can be written as `AB` (`A` concatenated with `B`), where `A` and `B` are VPS's, or
*   It can be written as `(A)`, where `A` is a VPS.

We can similarly define the _nesting depth_ `depth(S)` of any VPS `S` as follows:

*   `depth("") = 0`
*   `depth(A + B) = max(depth(A), depth(B))`, where `A` and `B` are VPS's
*   `depth("(" + A + ")") = 1 + depth(A)`, where `A` is a VPS.

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`