#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 998244353
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;
 
template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}



signed main(){
    int n;cin>>n;
    string s;cin>>s;

    ll res=0;

    using P=pair<ll,ll>;

    vector<P> v;

    ll p=0,ans=0,st=0;

    rep(i,n){
        if(s[i]=='(') st++;
        else{
            if(st==0) p++;
            else st--,ans+=n-i;
        }
        v.emplace_back(st,p);
    }

    sort(ALL(v),[](P a,P b){
        ll afs=a.second+max(0ll,b.second-a.first);
        ll bfs=b.second+max(0ll,a.second-b.first);
        if(afs!=bfs) return afs<bfs;
        return a.second<b.second;
    });

    ll x=0;
    for(auto &p:v){
        ll add=min(x,p.second);
        ans+=add,x-=add;
        x+=p.first;
    }

    cout<<ans*2<<endl;
    return 0;
}