# 1111. Maximum Nesting Depth of Two Valid Parentheses Strings

<https://leetcode.com/problems/maximum-nesting-depth-of-two-valid-parentheses-strings>

## Description

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`

## ac

```java
```