#include <bits/stdc++.h>
#define N 300000
using namespace std;
int a[300005];
vector<int> g[300005];
int sz[300005];
int del[300005];
void pre_dfs(int u, int p) {
sz[u] = 1;
for (int v: g[u]) {
if (v != p && del[v] == 0) {
pre_dfs(v, u);
sz[u] += sz[v];
}
}
}
int cent(int u, int p, int n) {
for (int v: g[u]) {
if (v != p && sz[v] > n / 2 && del[v] == 0) {
return cent(v, u, n);
}
}
return u;
}
int cnt[600005];
long long ans = 0;
void dfs(int u, int p, int s, int k, int type) {
if (type == 0) {
if (s == min(k, s)) {
ans += cnt[-s + N];
}
} else if (type == 1) {
if (min(a[u], a[u] + k) >= 0) {
cnt[s + N]++;
}
} else {
if (min(a[u], a[u] + k) >= 0) {
cnt[s + N]--;
}
}
for (int v: g[u]) {
if (v != p && del[v] == 0) {
if (type == 0) {
dfs(v, u, s + a[v], min(k, s), type);
} else {
dfs(v, u, s + a[v], min(a[u], a[u] + k), type);
}
}
}
}
void upd(int r) {
if (a[r] == 1) {
cnt[N + 1] = 1;
}
for (int v: g[r]) {
if (del[v] == 0) {
dfs(v, r, a[v], 0, 0);
dfs(v, r, a[r] + a[v], a[r], 1);
}
}
for (int v: g[r]) {
if (del[v] == 0) {
dfs(v, r, a[r] + a[v], a[r], 2);
}
}
if (a[r] == 1) {
cnt[N + 1] = 0;
}
}
void solve(int u) {
pre_dfs(u, u);
int r = cent(u, u, sz[u]);
upd(r);
del[r] = 1;
for (int v: g[r]) {
if (del[v] == 0) {
solve(v);
}
}
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int n;
cin >> n;
string s;
cin >> s;
s = '&' + s;
for (int i = 1; i <= n; ++i) {
a[i] = (s[i] == '(' ? 1 : -1);
}
for (int i = 1; i <= n - 1; ++i) {
int u, v;
cin >> u >> v;
g[u].emplace_back(v);
g[v].emplace_back(u);
}
memset(del, 0, sizeof del);
solve(1);
for (int i = 1; i <= n; ++i) {
a[i] *= -1;
}
memset(del, 0, sizeof del);
solve(1);
cout << ans << '\n';
}
