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
#include <bits/stdc++.h>
using namespace std;
int Set(int N, int pos) { return N = N | (1 << pos); }
int reset(int N, int pos) { return N = N & ~(1 << pos); }
bool check(int N, int pos) { return (bool)(N & (1 << pos)); }
int LR[1000006], RL[1000006], mnLR[1000006], mnRL[1000006];
int main() {
  int t = 1;
  while (t--) {
    int n;
    scanf("%d", &n);
    string s;
    cin >> s;
    for (int i = 0; i < s.size(); i++) {
      if (s[i] == '(') {
        if (i == 0)
          LR[i] = 1;
        else
          LR[i] = LR[i - 1] + 1;
      } else {
        if (i == 0)
          LR[i] = -1;
        else
          LR[i] = LR[i - 1] - 1;
      }
      mnLR[i] = LR[i];
      if (i) mnLR[i] = min(mnLR[i], mnLR[i - 1]);
    }
    for (int i = s.size() - 1; i >= 0; i--) {
      if (s[i] == '(') {
        RL[i] = RL[i + 1] - 1;
      } else {
        RL[i] = RL[i + 1] + 1;
      }
      mnRL[i] = RL[i];
      if (i != s.size() - 1) mnRL[i] = min(mnRL[i], mnRL[i + 1]);
    }
    int ans = 0;
    for (int i = 0; i < s.size(); i++) {
      if (s[i] == '(') {
        if (i) {
          if (RL[i + 1] == LR[i - 1] - 1 && mnLR[i - 1] >= 0 &&
              mnRL[i + 1] >= 0)
            ans++;
        }
      } else {
        if (i == 0) {
          if (RL[i + 1] == 1 && mnRL[i + 1] >= 0) ans++;
        } else if (i == s.size() - 1) {
        } else {
          if (RL[i + 1] - 1 == LR[i - 1] && mnLR[i - 1] >= 0 &&
              mnRL[i + 1] >= 0)
            ans++;
        }
      }
    }
    cout << ans;
  }
  return 0;
}
