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;
void test_case() {
  int n, i, cnt;
  cin >> n;
  string str;
  cin >> str;
  cnt = 0;
  vector<int> c(n + 5, 0);
  vector<int> flag(n + 5, 0);
  int fl = 0;
  for (i = n - 1; i >= 0; i--) {
    if (str[i] == '(')
      cnt++;
    else
      cnt--;
    c[i] = cnt;
    if (cnt > 0) fl = 1;
    flag[i] = fl;
  }
  cnt = 0;
  int ans = 0;
  fl = 0;
  for (i = 0; i < n; i++) {
    if (fl == 0 && str[i] == ')' && cnt + 1 == -c[i + 1] && cnt + 1 >= 0 &&
        flag[i + 1] == 0) {
      ans++;
    } else if (fl == 0 && str[i] == '(' && cnt - 1 == -c[i + 1] &&
               cnt - 1 >= 0 && flag[i + 1] == 0) {
      ans++;
    }
    if (str[i] == '(')
      cnt++;
    else if (str[i] == ')')
      cnt--;
    if (cnt < 0) fl = 1;
  }
  cout << ans << "\n";
  return;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  int t;
  t = 1;
  while (t--) {
    test_case();
  }
}
