#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll N = 300005;
ll n, tot, chi[N], a[N], ans;
bool blk[N];
char ipt[N];
vector<ll> adj[N];
map<ll, ll> pl, mi;
void calc (ll C, ll P) {
tot++;
chi[C] = 1;
for(auto &T : adj[C]) {
if(T == P || blk[T]) continue;
calc(T, C);
chi[C] += chi[T];
}
}
ll findcen (ll C, ll P) {
ll mx = 0;
for(auto &T : adj[C]) {
if(T == P || blk[T]) continue;
if(chi[mx] < chi[T]) mx = T;
}
if(chi[mx] <= tot/2) return C;
return findcen(mx, C);
}
void match (ll C, ll P, ll M, ll V, ll B, map<ll,ll> &S) {
if(V == M) ans += S[V];
for(auto &T : adj[C]) {
if(T == P || blk[T]) continue;
match(T, C, max(M, V+a[T]*B), V+a[T]*B, B, S);
}
}
void save (ll C, ll P, ll M, ll V, ll B, map<ll,ll> &S) {
if(V == M) S[V]++;
for(auto &T : adj[C]) {
if(T == P || blk[T]) continue;
save(T, C, max(M, V+a[T]*B), V+a[T]*B, B, S);
}
}
void solve (ll I) {
tot = 0; calc(I, 0);
ll C = findcen(I, 0);
pl.clear(); mi.clear();
pl[a[C]]++; mi[0]++;
for(auto &T : adj[C]) {
if(blk[T]) continue;
ll M1 = max({0ll, a[C], a[T]+a[C]}), M2 = max(0ll, -a[T]);
match(T, C, M1, a[T]+a[C], 1, mi);
match(T, C, M2, -a[T], -1, pl);
save(T, C, M1, a[T]+a[C], 1, pl);
save(T, C, M2, -a[T], -1, mi);
}
blk[C] = true;
for(auto &T : adj[C]) {
if(blk[T]) continue;
solve(T);
}
}
int main()
{
scanf("%lld%s",&n,ipt+1);
for(ll i=1;i<=n;i++) {
a[i] = 2*(ipt[i] == '(') - 1;
}
for(ll i=1;i<n;i++) {
ll A, B;
scanf("%lld%lld",&A,&B);
adj[A].push_back(B);
adj[B].push_back(A);
}
solve(1);
printf("%lld\n",ans);
}
