#include <bits/stdc++.h>
using namespace std;
int n, num[1100000], st[4400000];
string s;
void build(int a, int b, int index) {
  if (a == b)
    st[index] = num[a];
  else {
    build(a, (a + b) / 2, 2 * index);
    build((a + b) / 2 + 1, b, 2 * index + 1);
    st[index] = min(st[2 * index], st[2 * index + 1]);
  }
}
int query(int a, int b, int index, int l, int r) {
  if (a > r or b < l)
    return 1e9;
  else if (l <= a and b <= r) {
    return st[index];
  } else {
    return min(query(a, (a + b) / 2, 2 * index, l, r),
               query((a + b) / 2 + 1, b, 2 * index + 1, l, r));
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  cin >> s;
  int curr = 0;
  for (int i = 0; i < n; i++) {
    if (s[i] == '(')
      curr++;
    else
      curr--;
    num[i] = curr;
  }
  build(0, n - 1, 1);
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (s[i] == '(') {
      int minim = query(0, n - 1, 1, i, n - 1);
      if (num[n - 1] == 2 and minim >= 2) ans++;
    } else {
      int minim = query(0, n - 1, 1, i, n - 1);
      if (num[n - 1] == -2 and minim >= -2) ans++;
    }
    if (num[i] < 0) break;
  }
  cout << ans << endl;
}
