> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/1614-maximum-nesting-depth-of-the-parentheses.md).

# 1614. Maximum Nesting Depth of the Parentheses

<https://leetcode.com/problems/maximum-nesting-depth-of-the-parentheses>

## Description

A string is a **valid parentheses string** (denoted **VPS**) if it meets one of the following:

* It is an empty string `""`, or a single character not equal to `"("` 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(C) = 0`, where `C` is a string with a single character not equal to `"("` or `")"`.
* `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** represented as string `s`, return *the **nesting depth** of* `s`.

**Example 1:**

```
**Input:** s = "(1+(2*3)+((8)/4))+1"
**Output:** 3
**Explanation:** Digit 8 is inside of 3 nested parentheses in the string.
```

**Example 2:**

```
**Input:** s = "(1)+((2))+(((3)))"
**Output:** 3
```

**Example 3:**

```
**Input:** s = "1+(2*3)/(2-1)"
**Output:** 1
```

**Example 4:**

```
**Input:** s = "1"
**Output:** 0
```

**Constraints:**

* `1 <= s.length <= 100`
* `s` consists of digits `0-9` and characters `'+'`, `'-'`, `'*'`, `'/'`, `'('`, and `')'`.
* It is guaranteed that parentheses expression `s` is a **VPS**.

## ac

```java
```