# 0921. Minimum Add to Make Parentheses Valid

<https://leetcode.com/problems/minimum-add-to-make-parentheses-valid>

## Description

A parentheses string is valid if and only if:

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

You are given a parentheses string `s`. In one move, you can insert a parenthesis at any position of the string.

* For example, if `s = "()))"`, you can insert an opening parenthesis to be `"(**(**)))"` or a closing parenthesis to be `"())**)**)"`.

Return *the minimum number of moves required to make* `s` *valid*.

**Example 1:**

```
**Input:** s = "())"
**Output:** 1
```

**Example 2:**

```
**Input:** s = "((("
**Output:** 3
```

**Example 3:**

```
**Input:** s = "()"
**Output:** 0
```

**Example 4:**

```
**Input:** s = "()))(("
**Output:** 4
```

**Constraints:**

* `1 <= s.length <= 1000`
* `s[i]` is either `'('` or `')'`.

## ac

```java
```


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