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

using ll = long long;
using pll = pair<ll, ll>;
#define vc vector
using vl = vc<ll>;

#define ov(a, b, c, name, ...) name
#define rep2(i, l, r) for(ll i = (l); i < ll(r); i++)
#define rep1(i, n) rep2(i, 0, n)
#define rep(...) ov(__VA_ARGS__, rep2, rep1)(__VA_ARGS__)
#define fec(...) for(const auto& __VA_ARGS__)
#define per(i, a, b) for(ll i = ll(a) - 1; i >= ll(b); i--)

#define ALL(x) begin(x), end(x)
#define SZ(x) (ll) size(x)
#define LB(v, x) (lower_bound(ALL(v), x) - begin(v))
#define eb emplace_back

bool chmin(auto& a, auto b) { return a > b ? a = b, 1 : 0; }
bool chmax(auto& a, auto b) { return a < b ? a = b, 1 : 0; }
const ll INF = ll(4e18) + 100;

void printvec(const auto& v) {
   for(auto it = begin(v); it != end(v); it++) cout << *it << " ";
   cout << endl;
}

#ifdef LOCAL
#define local(...) __VA_ARGS__
#else
#define local(...)
#endif

struct S {
   ll c0, c1, inv = 0;
   deque<int> p{};
   bool operator>(S &r) const {
    if (c0 == 0 && c1 == 0)
      return false;
    if (r.c0 == 0 && r.c1 == 0)
      return true;
    return c1 * r.c0 > c0 * r.c1;
   }
   void merge(S &r) {
    inv += r.inv + c1 * r.c0, c0 += r.c0, c1 += r.c1;
    if (p.size() > r.p.size()) {
      while (!r.p.empty()) p.push_back(r.p.front()), r.p.pop_front();
    } else {
      swap(p, r.p);
      while (!r.p.empty()) p.push_front(r.p.back()), r.p.pop_back();
    }
  }
};
auto zotree(vc<S> &s, const auto &g) {
  auto comp = [](S *a, S *b)
  { return *a > *b; };
  using PQ = priority_queue<S *, vc<S *>, decltype(comp)>;
  auto dfs = [&](auto dfs, int p, int pp) -> PQ
  {
    PQ pq{comp};
    fec(e : g[p])
    {
      if (pp == e)
        continue;
      auto ch = dfs(dfs, e, p);
      if (pq.size() < ch.size())
        pq.swap(ch);
      while (!ch.empty())
        pq.push(ch.top()), ch.pop();
    }
    while (!pq.empty() && !(*pq.top() > s[p]))
      s[p].merge(*pq.top()), pq.pop();
    pq.push(&s[p]);
    return pq;
  };
  auto pq = dfs(dfs, 0, -1); // 0 が root
  S res(0, 0);
  while (!pq.empty())
    res.merge(*pq.top()), pq.pop();
  return res;
}

void main2() {
  ll N;
  cin >> N;
  string T;
  cin >> T;
  vc<S> s(N + 1);
  s.at(0) = {1, 1};
  rep(i, 1, N + 1)
  {
    cin >> s.at(i).c0;
    s.at(i).c1 = 1;
  }

  vc<vl> G(1);
  vl sta{0};
  fec(c : T) {
    local(

        cout << "sta= ";
        printvec(sta);
        rep(i, G.size()) {
          cout << i << "  ";
          printvec(G.at(i));
        }

    );
    if (c == '(')
    {
      ll v = sta.back();
      ll nv = G.size();
      G.eb();
      G.at(v).eb(nv);
      sta.eb(nv);
    }
    else
    {
      sta.pop_back();
    }
  }

  ll ans = zotree(s, G).inv;
  cout << ans << "\n";
}

int main() {
#ifndef LOCAL
  cin.tie(0)->sync_with_stdio(0), cout.tie(0);
#endif

  local(while (true)) {
    ll t = 1;
    // cin >> t;
    while(t--) main2();
  }
}