#include <bits/stdc++.h>
using namespace std;
const int N = (int) 3e5 + 9;
int n;
string a;
vector<int> g[N];
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n >> a;
for (int i = 1; i < n; i++) {
int u, v;
cin >> u >> v;
--u; --v;
g[u].push_back(v);
g[v].push_back(u);
}
if (n <= 1000) {
function<int(int, int, int)> DFS = [&](int v, int pr, int bal) {
bal += (a[v] == '(') - (a[v] == ')');
if (bal < 0) {
return 0;
}
int ret = !bal;
for (int u : g[v]) {
if (u == pr) {
continue;
}
ret += DFS(u, v, bal);
}
return ret;
};
int ans = 0;
for (int i = 0; i < n; i++) {
ans += DFS(i, -1, 0);
}
cout << ans << '\n';
} else {
long long ans = 0;
for (int itr = 0; itr < 2; itr++) {
reverse(a.begin(), a.end());
vector<pair<char, int>> stk;
for (int i = 0; i < n; i++) {
if (a[i] == ')') {
while (!stk.empty() && stk.back().first == ')') {
stk.pop_back();
}
if (stk.empty()) {
continue;
}
stk.back().first = ')';
stk.back().second += 1;
ans += stk.back().second;
} else {
if (stk.empty()) {
stk.push_back({'(', 0});
continue;
}
if (stk.back().first == '(') {
stk.push_back({'(', 0});
continue;
}
stk.push_back({'(', stk.back().second});
}
}
}
cout << ans << '\n';
}
return 0;
}
