/**
* author: wxhtzdy
* created: 30.06.2022 10:05:38
**/
#include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n;
cin >> n;
string s;
cin >> s;
vector<vector<int>> g(n);
for (int i = 0; i < n - 1; i++) {
int u, v;
cin >> u >> v;
--u; --v;
g[u].push_back(v);
g[v].push_back(u);
}
vector<bool> was(n);
vector<int> sz(n);
function<void(int, int)> Dfs = [&](int v, int pr) {
sz[v] = 1;
for (int u : g[v]) {
if (u == pr || was[u]) {
continue;
}
Dfs(u, v);
sz[v] += sz[u];
}
};
function<int(int, int, int)> Find = [&](int v, int pr, int n) {
for (int u : g[v]) {
if (u == pr || was[u] || sz[u] * 2 < n) {
continue;
}
return Find(u, v, n);
}
return v;
};
map<int, int> cnt;
long long ans = 0;
function<void(int, int, int, int, int)> Go = [&](int v, int pr, int bal, int mn, int f) {
int me = (s[v] == '(' ? 1 : -1);
bal += me;
mn = min(me, me + mn);
if (mn >= 0) {
cnt[bal] += f;
}
for (int u : g[v]) {
if (u == pr || was[u]) {
continue;
}
Go(u, v, bal, mn, f);
}
};
function<void(int, int, int, int)> Run = [&](int v, int pr, int bal, int mn) {
bal += (s[v] == '(' ? +1 : -1);
mn = min(mn, bal);
if (mn == 0 && bal == 0) {
ans += 1;
}
if (-bal + mn >= 0) {
ans += cnt[-bal];
}
for (int u : g[v]) {
if (u == pr || was[u]) {
continue;
}
Run(u, v, bal, mn);
}
};
function<void(int)> Solve = [&](int v) {
Dfs(v, v);
v = Find(v, v, sz[v]);
was[v] = true;
cnt.clear();
for (int u : g[v]) {
if (was[u]) {
continue;
}
Go(u, v, 0, 1, +1);
}
if (s[v] == ')') {
ans += cnt[1];
}
for (int u : g[v]) {
if (was[u]) {
continue;
}
int me = (s[v] == '(' ? +1 : -1);
Go(u, v, 0, 1, -1);
Run(u, v, me, me);
Go(u, v, 0, 1, +1);
}
for (int u : g[v]) {
if (!was[u]) {
Solve(u);
}
}
};
Solve(0);
cout << ans << '\n';
return 0;
}
