#include <bits/stdc++.h>
using namespace std;
int count(string s, int idx, char c, int d) {
  int ret = 0;
  for (int i = idx + d; i < s.length() && i >= 0; i += d) {
    if (s[i] == c) ret++;
  }
  return ret;
}
int main() {
  int n;
  string s;
  cin >> n >> s;
  stack<int> st;
  for (int i = 0; i < n; i++) {
    if (!st.empty() && s[st.top()] == '(' && s[i] == ')')
      st.pop();
    else
      st.push(i);
  }
  if (st.size() == 2) {
    int a = st.top();
    st.pop();
    int b = st.top();
    int ans = 0;
    if (s[a] == '(' && s[b] == ')')
      cout << "0";
    else if (s[a] == '(') {
      for (int i = a; i < s.length(); i++) {
        if (s[i] == '(') ans++;
      }
      cout << ans;
    } else {
      for (int i = b; i >= 0; i--) {
        if (s[i] == ')') ans++;
      }
      cout << ans;
    }
  } else
    cout << "0";
  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

You are given a bracket sequence s consisting of n opening '(' and closing ')' brackets.

A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.

You can change the type of some bracket s_i. It means that if s_i =  ')' then you can change it to '(' and vice versa.

Your task is to calculate the number of positions i such that if you change the type of the i-th bracket, then the resulting bracket sequence becomes regular.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 10^6) — the length of the bracket sequence.

The second line of the input contains the string s consisting of n opening '(' and closing ')' brackets.

Output

Print one integer — the number of positions i such that if you change the type of the i-th bracket, then the resulting bracket sequence becomes regular.

Examples

Input


6
(((())


Output


3


Input


6
()()()


Output


0


Input


1
)


Output


0


Input


8
)))(((((


Output


0

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int count(string s, int idx, char c, int d) {
  int ret = 0;
  for (int i = idx + d; i < s.length() && i >= 0; i += d) {
    if (s[i] == c) ret++;
  }
  return ret;
}
int main() {
  int n;
  string s;
  cin >> n >> s;
  stack<int> st;
  for (int i = 0; i < n; i++) {
    if (!st.empty() && s[st.top()] == '(' && s[i] == ')')
      st.pop();
    else
      st.push(i);
  }
  if (st.size() == 2) {
    int a = st.top();
    st.pop();
    int b = st.top();
    int ans = 0;
    if (s[a] == '(' && s[b] == ')')
      cout << "0";
    else if (s[a] == '(') {
      for (int i = a; i < s.length(); i++) {
        if (s[i] == '(') ans++;
      }
      cout << ans;
    } else {
      for (int i = b; i >= 0; i--) {
        if (s[i] == ')') ans++;
      }
      cout << ans;
    }
  } else
    cout << "0";
  return 0;
}

```