#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;
}
