#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pii;
#define all(x) x.begin(), x.end()
#define sz(x) ((int) ((x).size()))
#define pb push_back
#define F first
#define S second
#define FIO ios_base::sync_with_stdio(false); cin.tie(0)
const int N = 3e5 + 10;
int n;
string s;
vector<int> adj[N];
ll ans;
bool done[N];
int sz[N];
int count(int node, int prev) {
sz[node] = 1;
for (int x : adj[node]) {
if (x == prev or done[x]) continue;
sz[node] += count(x, node);
}
return sz[node];
}
int find(int node, int vel, int prev) {
for (int x : adj[node]) {
if (x == prev or done[x]) continue;
if (sz[x] * 2 > vel) return find(x, vel, node);
}
return node;
}
ll cnt[N];
void add(int node, int prev, int cur, int have, int need, int mode) {
if (s[node - 1] == ')') {
if (mode == 0) {
if (cur == 0) need++;
else cur--;
} else {
cur--;
}
} else {
if (mode == 0) {
cur++;
} else {
if (cur == 0) have++;
else cur++;
}
}
if (mode and cur == 0) cnt[have] += mode;
if (mode == 0 and cur == 0) ans += cnt[need];
for (int x : adj[node]) {
if (done[x] or x == prev) continue;
add(x, node, cur, have, need, mode);
}
}
void run(int node) {
int cen = find(node, count(node, 0), 0);
done[cen] = 1;
int cur = 0, have = 0, need = 0;
if (s[cen - 1] == ')') {
cur--;
} else {
if (cur == 0) have++;
else cur++;
}
add(cen, 0, 0, 0, 0, 1);
ans += cnt[0];
for (int x : adj[cen]) {
if (done[x]) continue;
add(x, cen, cur, have, need, -1);
add(x, cen, 0, 0, 0, 0);
add(x, cen, cur, have, need, 1);
}
add(cen, 0, 0, 0, 0, -1);
for (int x : adj[cen]) {
if (done[x]) continue;
run(x);
}
}
int main() {
FIO;
cin >> n >> s;
for (int i = 0; i < n - 1; i++) {
int a, b;
cin >> a >> b;
adj[a].pb(b);
adj[b].pb(a);
}
run(1);
cout << ans << '\n';
return 0;
}
