# [Solved] A valid parentheses string is either empty “”, “(” + A + “)”, or A + B, where A and B are valid parentheses strings, and + represents string concatenation. ## Question

A valid parentheses string is either empty `""``"(" + A + ")"`, or `A + B`, where `A` and `B` are valid parentheses strings, and `+` represents string concatenation.

• For example, `""``"()"``"(())()"`, and `"(()(()))"` are all valid parentheses strings.

A valid parentheses string `s` is primitive if it is nonempty, and there does not exist a way to split it into `s = A + B`, with `A` and `B` nonempty valid parentheses strings.

Given a valid parentheses string `s`, consider its primitive decomposition: `s = P1 + P2 + ... + Pk`, where `Pi` are primitive valid parentheses strings.

Return `s` after removing the outermost parentheses of every primitive string in the primitive decomposition of `s`.

Example 1:

```Input: s = "(()())(())"
Output: "()()()"
Explanation:
The input string is "(()())(())", with primitive decomposition "(()())" + "(())".
After removing outer parentheses of each part, this is "()()" + "()" = "()()()".
```

Example 2:

```Input: s = "(()())(())(()(()))"
Output: "()()()()(())"
Explanation:
The input string is "(()())(())(()(()))", with primitive decomposition "(()())" + "(())" + "(()(()))".
After removing outer parentheses of each part, this is "()()" + "()" + "()(())" = "()()()()(())".
```

Example 3:

```Input: s = "()()"
Output: ""
Explanation:
The input string is "()()", with primitive decomposition "()" + "()".
After removing outer parentheses of each part, this is "" + "" = "".
```

Constraints:

• `1 <= s.length <= 105`
• `s[i]` is either `'('` or `')'`.
• `s` is a valid parentheses string.

## Python Solution

```class Solution:
def removeOuterParentheses(self, S: str) -> str:
opened=0
res=''

for c in S:
if c=='(' and opened>0:res+=c
if c==')' and opened>1:res+=c
opened += 1 if c == '(' else -1
return res```