#include <cstdio>
#include <vector>
#include <algorithm>

using int64 = long long;

const int N = 1e5 + 10;

struct node {
  int64 p, q;
  bool operator < (const node &t) const{
    if (q >= 0 && t.q >= 0) return p > t.p;
    return q > t.q;
  }
};

char S[N];
int n;

int main() {
  scanf ("%d%s", &n, S);
  int64 b = 0, mn = 0;
  std::vector<node> V(n);
  for (int i = 0; i < n; i++) {
    if (S[i] == '(') b++;
    else {
      b--;
      if (mn > b) mn = b;
    }
    V[i] = {mn,b};
  }
  std::sort(V.begin(), V.end());
  int64 ab = 0, amn = 0;
  for (int i = 0; i < n; i++){
    if (amn > ab + V[i].p) {
      amn = ab + V[i].p;
    }
    ab += V[i].q;
  }

  int64 len = (int64)n * (n + 1) / 2 - ab + 2 * amn;
  printf ("%lld\n", len);
  return 0;
}