#include<bits/stdc++.h>
#include<atcoder/segtree>
using namespace std;

int op_min(int a, int b){
  return min(a, b);
}

int e_min(){
  return (int)(1e9);
}

int op_max(int a, int b){
  return max(a, b);
}

int e_max(){
  return (int)(-1e9);
}

int main(){

  int N;
  cin >> N;
  string S;
  cin >> S;
  S += '?';
  N++;

  vector<int>max_r(N + 1);
  {
    vector<int>B(N + 1);
    for(int i = 0; i < N; i++){
      B[i + 1] = B[i] + (S[i] == ')' ? -1 : 1);
    }
    atcoder::segtree<int,op_min,e_min>seg(B);
    for(int i = 0; i < N; i++){
      auto judge = [&](int x){
        return x >= B[i];
      };
      max_r[i] = seg.max_right<decltype(judge)>(i, judge);
    }
  }
  vector<int>min_l(N + 1);
  {
    vector<int>B(N + 1);
    for(int i = 0; i < N; i++){
      B[i + 1] = B[i] + (S[i] == '(' ? 1 : -1);
    }
    atcoder::segtree<int,op_min,e_min>seg(B);
    for(int i = 0; i < N; i++){
      auto judge = [&](int x){
        return x >= B[i];
      };
      min_l[i] = seg.min_left<decltype(judge)>(i, judge);
    }
  }
  using Seg = atcoder::segtree<int,op_max,e_max>;
  vector<Seg> dp1(2, Seg(N + 1));
  vector<Seg> dp2(2, Seg(N + 1));
  dp1[0].set(0,0);
  vector<vector<int>>del(N + 2);
  for(int i = 0; i < N; i++){
    del[max_r[i]].push_back(i);
  }
  for(int r = 0; r < N; r++){
    for(auto l: del[r]){
      for(int j = 0; j < 2; j++){
        dp1[j].set(l, e_max());
        dp2[j].set(l, e_max());
      }
    }
    int mx1 = max(dp1[r % 2].get(r), dp1[r % 2].prod(min_l[r], r) + 1);
    int mx2 = max(dp2[r % 2].get(r), dp2[r % 2].prod(max(0, min_l[r] - 2), r) + 1);
    if(S[r] != '(')dp1[(r + 1) % 2].set(r + 1, mx1);
    if(S[r] != ')')dp2[(r + 1) % 2].set(r + 1, max(mx1, mx2));
  }
  cout << dp2[N % 2].get(N) << endl;
  return 0;
}