#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

ll n;
string s;
vector<pair<ll,ll> > a,b;

int main(){
	cin>>n>>s;
	assert(1<=n&&n<=100000);
	assert(s.size()==n);
	ll t=0,m=0,S=0;
	for(int i=0;i<n;i++){
	    assert(s[i]=='('||s[i]==')');
		ll d=(s[i]=='('?1:-1);
		t+=d;
		S+=d*(n-i);
		m=min(m,t);
		if(t>=0) a.push_back({-m,t});
		else b .push_back({m-t,t});
	}
	sort(a.begin(),a.end());
	sort(b.begin(),b.end());
	t=0,m=0;
	for(int i=0;i<a.size();i++){
		ll A=a[i].first,B=a[i].second;
		m=min(m,t-A);
		t+=B;
	}
	for(int i=0;i<b.size();i++){
		ll A=b[i].first,B=b[i].second;
		m=min(m,t+A+B);
		t+=B;
	}
	cout<<n*(n+1)/2+2*m-t<<endl;
}