# Maximum Nesting Depth of the Parentheses

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(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.

Solution:

```class Solution {
/*
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.
*/
public int maxDepth(String s) {
int left = 0, max = 0;
for (int i = 0; i < s.length(); i ++) {
char c = s.charAt(i);
if (c == '(') {
left ++;
max = Math.max(max, left);
}
if (c == ')') {
left --;
}
}
return max;
}
}```