#include <bits/stdc++.h>
using namespace std;
int Left[1000010];
int mini[1000010];
int main(void) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  string S;
  cin >> S;
  for (int i = 0; i < S.length(); i++) {
    if (S[i] == '(')
      Left[i + 1] = Left[i] + 1;
    else
      Left[i + 1] = Left[i] - 1;
  }
  for (int i = 0; i < 1000010; i++) mini[i] = 2000000000;
  int ans = 0;
  if (Left[n] == 2) {
    for (int i = n; i >= 0; i--) mini[i] = min(mini[i + 1], Left[i]);
    for (int i = 0; i < n; i++) {
      if (i != 0 && Left[i - 1] < 0) break;
      if (S[i] == '(' && mini[i + 1] >= 2 && Left[n] == 2) ans++;
    }
  } else if (Left[n] == -2) {
    for (int i = n; i >= 0; i--) mini[i] = min(mini[i + 1], Left[i]);
    for (int i = 0; i < n - 1; i++) {
      if (i != 0 && Left[i - 1] < 0) break;
      if (S[i] == ')' && mini[i] >= -2) ans++;
    }
  }
  cout << ans << endl;
  return 0;
}
