#include <bits/stdc++.h>
using namespace std;
const int MAX_N = 300'000 + 10;
int n, val[MAX_N], cnt[MAX_N];
vector<int> adj[MAX_N];
long long ans;
int sz[MAX_N];
bool mark[MAX_N];
void size_dfs(int u, int p) {
sz[u] = 1;
for (int v : adj[u]) {
if (!mark[v] && v != p) {
size_dfs(v, u);
sz[u] += sz[v];
}
}
}
int find_cent(int u, int p, int root) {
for (int v : adj[u]) {
if (!mark[v] && v != p && sz[v] > sz[root] / 2) {
return find_cent(v, u, root);
}
}
return u;
}
void add_dfs(int u, int p, int curr, int mx, vector<int>& rm) {
curr += val[u];
mx = max(mx, curr);
if (mx == curr) {
++cnt[curr];
rm.push_back(curr);
}
for (int v : adj[u]) {
if (!mark[v] && v != p) {
add_dfs(v, u, curr, mx, rm);
}
}
}
void count_dfs(int u, int p, int curr, int mn) {
curr += val[u];
mn = min(mn, curr);
if (mn == curr) {
ans += cnt[-curr];
}
for (int v : adj[u]) {
if (!mark[v] && v != p) {
count_dfs(v, u, curr, mn);
}
}
}
void decompose(int v) {
size_dfs(v, -1);
v = find_cent(v, -1, v);
vector<int> rm;
if (val[v] == 1) ++cnt[1];
for (int u : adj[v]) {
if (!mark[u]) {
count_dfs(u, v, 0, 0);
add_dfs(u, v, val[v], max(0, val[v]), rm);
}
}
ans += cnt[0];
for (int x : rm) {
--cnt[x];
}
rm.clear();
if (val[v] == 1) --cnt[1];
reverse(adj[v].begin(), adj[v].end());
for (int u : adj[v]) {
if (!mark[u]) {
count_dfs(u, v, 0, 0);
add_dfs(u, v, val[v], max(0, val[v]), rm);
}
}
for (int x : rm) {
--cnt[x];
}
mark[v] = true;
for (int u : adj[v]) {
if (!mark[u]) {
decompose(u);
}
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr), cout.tie(nullptr);
cin >> n;
for (int u = 1; u <= n; ++u) {
char c;
cin >> c;
if (c == '(') val[u] = +1;
else val[u] = -1;
}
for (int e = 1, u, v; e <= n - 1; ++e) {
cin >> u >> v;
adj[u].push_back(v);
adj[v].push_back(u);
}
decompose(1);
cout << ans << '\n';
}
