#include<deque>
#include<queue>
#include<vector>
#include<algorithm>
#include<iostream>
#include<set>
#include<cmath>
#include<tuple>
#include<string>
#include<chrono>
#include<functional>
#include<iterator>
#include<random>
#include<unordered_set>
#include<array>
#include<map>
#include<iomanip>
using namespace std;
typedef long long int llint;
typedef long double lldo;
#define mp make_pair
#define mt make_tuple
#define pub push_back
#define puf push_front
#define pob pop_back
#define pof pop_front
#define fir first
#define sec second
#define res resize
#define ins insert
#define era erase
//cout<<setprecision(20)
const llint mod=1000000007;
const llint big=2.19e15+1;
const long double pai=3.141592653589793238462643383279502884197;
const long double eps=1e-15;
template <class T,class U>void mineq(T& a,U b){if(a>b){a=b;}}
template <class T,class U>void maxeq(T& a,U b){if(a<b){a=b;}}
llint gcd(llint a,llint b){if(a%b==0){return b;}else return gcd(b,a%b);}
llint lcm(llint a,llint b){return a/gcd(a,b)*b;}
template<class T> void SO(T& ve){sort(ve.begin(),ve.end());}
template<class T> void REV(T& ve){reverse(ve.begin(),ve.end());}
int LBI(vector<llint>&ar,llint in){return lower_bound(ar.begin(),ar.end(),in)-ar.begin();}
int UBI(vector<llint>&ar,llint in){return upper_bound(ar.begin(),ar.end(),in)-ar.begin();}
int main(void){
	llint n,i;cin>>n;
	string str;cin>>str;
	vector<pair<llint,llint>>subue;
	vector<pair<llint,llint>>subst;
	llint gen=0,sai=0;
	for(i=0;i<n;i++){
		if(str[i]=='('){gen++;}else{gen--;}
		mineq(sai,gen);
		if(gen>=0){subue.pub(mp(sai,gen));}
		else{subst.pub(mp(sai,gen));}
	}
	sai=0;gen=0;
	SO(subue);
	SO(subst);REV(subst);
	//上方向を使い切る->下方向
	for(auto it:subue){
		mineq(sai,gen+it.fir);
		gen+=it.sec;
	}
	for(auto it:subst){
		mineq(sai,gen+it.fir);
		gen+=it.sec;
	}
	llint ans=n*(n+1)/2;
	ans-=gen;
	ans+=sai*2;
	cout<<ans<<endl;
}