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

class UnionFind{
    private:
    vector<int> par,siz;
    public:
    UnionFind(int N){par.resize(N,-1);}
    int root(int x){ //連結成分の代表頂点を返す.
        if(par.at(x) == -1) return x;
        else return par.at(x) = root(par.at(x));
    }
    bool unite(int u, int v){ //u,vを連結する 連結してた->false,した->trueを返す.
        u = root(u),v = root(v);
        if(u == v) return false;
        par.at(u) = v;
        return true;
    }
    bool issame(int u, int v){ //同じ連結成分ならtrue.
        if(root(u) == root(v)) return true;
        else return false;
    }
};

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
 
    int N; cin >> N;
    string s; cin >> s;
    vector<int> par(N+1,-1);
    int idx = 0;
    stack<int> St; St.push(idx);
    for(auto c : s){
        if(c == '('){
            idx++;
            par.at(idx) = St.top(); St.push(idx);
        }
        else St.pop();
    }

    vector<long long> A(N+1),B(N+1,1);
    for(int i=1; i<=N; i++) cin >> A.at(i);

    using T = tuple<long long,long long,int>;
    auto comp = [&](const T &a,const T &b) -> bool {
        auto [x,y,p] = a;
        auto [x2,y2,q] = b;
        return x*y2 < x2*y;
    };
    priority_queue<T,vector<T>,decltype(comp)> Q(comp);
    for(int i=1; i<=N; i++) Q.push({A.at(i),B.at(i),i});
    UnionFind Z(N+1);
    long long answer = 0;
    while(Q.size()){
        auto [a,b,pos] = Q.top(); Q.pop();
        if(A.at(pos) != a || B.at(pos) != b) continue;
        Z.unite(pos,par.at(pos));
        int leader = Z.root(pos);
        long long &a2 = A.at(leader),&b2 = B.at(leader);
        answer += b2*a; a2 += a; b2 += b;
        if(leader != 0) Q.push({a2,b2,leader});
    }
    cout << answer << endl;
}