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;
const int N = 1000000 + 1000;
const int MOD = 1e9 + 7;
const double PI = acos(-1.0);
const double EXP = 1E-8;
const int INF = 0x3f3f3f3f;
int t, n, m, k, q;
char str[N];
int a[N];
int b[N];
int main() {
  scanf("%d", &n);
  scanf("%s", str);
  if (n % 2) {
    cout << 0 << endl;
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (i) a[i] = a[i - 1];
    if (str[i] == '(')
      a[i]++;
    else
      a[i]--;
    if (a[i] < -2) {
      cout << 0 << endl;
      return 0;
    }
  }
  int flag = 0;
  for (int i = n - 1; i >= 0; i--) {
    b[i] = b[i + 1];
    if (str[i] == '(')
      b[i]++;
    else
      b[i]--;
    if (b[i] > 0 && !flag) {
      flag = i;
    }
    if (b[i] > 2) {
      cout << 0 << endl;
      return 0;
    }
  }
  if (abs(b[0]) != 2) {
    cout << 0 << endl;
    return 0;
  }
  int ans = 0;
  for (int i = flag; i < n; i++) {
    if (i != 0 && str[i] == '(') {
      if (a[i] - 2 + b[i + 1] == 0 && a[i] - 2 >= 0 && b[i] - 2 <= 0) ans++;
    } else if (i != n - 1 && str[i] == ')') {
      if (a[i] + 2 + b[i + 1] == 0 && a[i] + 2 >= 0 && b[i] + 2 <= 0) ans++;
    }
    if (a[i] < 0) {
      break;
    }
  }
  cout << ans << endl;
  return 0;
}
