#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;

        parents[x] += parents[y];
        parents[y] = x;
        ans += ones[x] * zeros[y];
        zeros[x] += zeros[y];
        ones[x] += ones[y];
    }

    int size(int x) {
        return -parents[find(x)];
    }

    bool same(int x, int y) {
        return find(x) == find(y);
    }
};

int main() {
    int N;
    cin >> N;
    string S;
    cin >> S;
    vector<int> A(N + 1);
    A[0] = 0;
    for (int i = 1; i <= N; ++i) cin >> A[i];

    UnionFind uf(A);

    vector<int> stack = {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] = stack.back();
            stack.push_back(next_idx++);
        } else {
            stack.pop_back();
        }
    }

    // 優先度付きキュー (最大ヒープ)
    using T = pair<double, int>;
    priority_queue<T> pq;
    for (int i = 0; i <= N; ++i) {
        pq.emplace((double)(-A[i]), i);
    }

while (!pq.empty()) {
    auto [value, idx] = pq.top(); pq.pop();
    int rep = uf.find(idx);
    double current_value = -(double)uf.zeros[rep] / uf.ones[rep];
    if (value != current_value) continue;

    uf.unite(uf.find(parent[rep]), rep);
    int new_head = uf.find(rep);
    if (new_head != 0) {
        double new_val = -(double)uf.zeros[new_head] / uf.ones[new_head];
        pq.emplace(new_val, new_head);
    }
}
    cout << uf.ans << endl;
    return 0;
}