#include <bits/stdc++.h>

using namespace std;
 
#define DEBUG(x) cout<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cout<<#v<<":";for(int i=0;i<v.size();i++) cout<<" "<<v[i]; cout<<endl
 
typedef long long ll;
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
#define fi first
#define se second
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define all(c) c.begin(),c.end()
#define in(x, a, b) a <= x && x < b
const int inf = 1000000001;
const ll INF = 2e18;
const ll MOD = 1000000007;
//const ll mod = 1000000009;
const double pi = 3.14159265358979323846;
#define Sp(p) cout<<setprecision(15)<< fixed<<p <<endl;
int dx[4] = { 1,0, -1,0 }, dy[4] = { 0,1,0,-1 };
int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };


bool cmp(pll a, pll b) {
  return min(a.second, b.first) > min(b.second, a.first);
}


int main() {
  int n;
  cin >> n;
  string s;
  cin >> s;
  ll ans = 0;
  vector<pll> num(n);
  string t;
  pll numnow = pll(0, 0);
  int delnow = 0;
  rep (i, n) {
    t.push_back(s[i]);
    if (s[i] == '(') {
      numnow.first++;
    }
    else {
      numnow.second++;
    }
    if (t.size() >= 2 && t.substr(t.size() - 2, 2) == "()") {
      delnow++;
      t.pop_back(); t.pop_back();
      numnow.first--; numnow.second--;
    }
    ans += delnow;
    num[i] = numnow;
  }
  sort(all(num), cmp);
  ll now = 0;
  rep (i, n) {
    ll used = min(now, num[i].first);
    ans += used;
    now -= used;
    now += num[i].second;
  }
  cout << ans * 2 << endl;
}