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

#undef _P
#define _P(...) (void)printf(__VA_ARGS__)
#define FOR(x,to) for(x=0;x<(to);x++)
#define FORR(x,arr) for(auto& x:arr)
#define ITR(x,c) for(__typeof(c.begin()) x=c.begin();x!=c.end();x++)
#define ALL(a) (a.begin()),(a.end())
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
//-------------------------------------------------------

int N;
string S;
int A[101010],B[101010],C[101010];
ll ret;
vector<pair<ll,ll>> V;

bool cmp(pair<ll,ll> L,pair<ll,ll> R) {
	return minmax(-L.first,-L.first+L.second-R.first) > minmax(-R.first,-R.first+R.second-L.first);
}


void solve() {
	int i,j,k,l,r,x,y; string s;
	
	cin>>N>>S;
	FOR(i,N) {
		A[i+1]=A[i];
		B[i+1]=B[i];
		C[i+1]=C[i];
		if(S[i]=='(') {
			B[i+1]++;
		}
		else {
			if(B[i+1]) {
				B[i+1]--;
				C[i+1]++;
			}
			else {
				A[i+1]++;
			}
		}
		ret+=C[i+1];
		V.push_back({A[i+1],B[i+1]});
	}
	
	sort(ALL(V),cmp);
	ll cur=0;
	FORR(v,V) {
		ret+=min(cur,v.first);
		cur-=min(cur,v.first);
		cur+=v.second;
	}
	cout<<ret*2<<endl;
	
}


int main(int argc,char** argv){
	string s;int i;
	if(argc==1) ios::sync_with_stdio(false), cin.tie(0);
	FOR(i,argc-1) s+=argv[i+1],s+='\n'; FOR(i,s.size()) ungetc(s[s.size()-1-i],stdin);
	cout.tie(0); solve(); return 0;
}