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

struct UnionFind {
    int N;
    vector<int> parents;
    vector<long long> zeros;
    vector<int> ones;
    long long ans;

    UnionFind(const vector<int>& A) {
        N = A.size();
        parents.assign(N, -1);
        zeros = vector<long long>(A.begin(), A.end());
        ones.assign(N, 1);
        ans = 0;
    }

    int find(int x) {
        if (parents[x] < 0) return x;
        vector<int> st;
        while (parents[x] >= 0) {
            st.push_back(x);
            x = parents[x];
        }
        for (int y : st) parents[y] = x;
        return x;
    }

    void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if (x == y) return;

        // x に y をマージ
        parents[x] += parents[y];
        parents[y] = x;
        ans += ones[x] * zeros[y];
        zeros[x] += zeros[y];
        ones[x] += ones[y];
    }
};

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int N;
    cin >> N;
    string S;
    cin >> S;

    // A[0] = 0, A[1..N] は入力
    vector<int> A(N + 1);
    A[0] = 0;
    for (int i = 1; i <= N; ++i) {
        cin >> A[i];
    }

    UnionFind uf(A);

    // 木構造の親を構築
    vector<int> stk = {0};
    vector<int> parent(N + 1, -1);
    int next_idx = 1;
    for (int i = 0; i < 2 * N; ++i) {
        if (S[i] == '(') {
            parent[next_idx] = stk.back();
            stk.push_back(next_idx++);
        } else {
            stk.pop_back();
        }
    }

    // (比率, idx) の最小ヒープ
    using P = pair<double,int>;
    priority_queue<P, vector<P>, greater<P>> pq;
    for (int i = 0; i <= N; ++i) {
        // 初期値: -(zeros[i]/ones[i]) = -A[i]/1
        pq.emplace(-(double)A[i], i);
    }

    while (!pq.empty()) {
        auto [value, idx] = pq.top();
        pq.pop();

        // Python版と同じく "idx" に対してチェック
        double current = -(double)uf.zeros[idx] / uf.ones[idx];
        if (value != current) continue;

        // union(parent[idx], idx)
        uf.unite(parent[idx], idx);

        // マージ後の代表元を取得
        int head = uf.find(idx);
        if (head != 0) {
            double nw = -(double)uf.zeros[head] / uf.ones[head];
            pq.emplace(nw, head);
        }
    }

    cout << uf.ans << "\n";
    return 0;
}