///In the name of GOD
#pragma GCC optimize("O2")
#include<bits/stdc++.h>
using namespace std;
//typedef long long ll;
typedef int ll;
const ll MXN = 3e5 + 10;
ll n, globc;
long long ans;
ll sub[MXN], bal[MXN], minb[MXN], ted[MXN];
vector<ll> adj[MXN];
bool hide[MXN];
string s;
void plant(ll u, ll par){
sub[u] = 1;
for(auto v : adj[u]){
if(v != par && !hide[v]){
plant(v, u), sub[u] += sub[v];
}
}
}
ll CRD(ll u, ll par, ll val){
for(auto v : adj[u]){
if(v == par || hide[v]) continue;
if(sub[v] >= val) return CRD(v, u, val);
}
return u;
}
void Upd(ll u, ll par, ll dt){
if(par == globc) bal[u] = minb[u] = 0;
else bal[u] = bal[par], minb[u] = minb[par];
bal[u] += (s[u] == '(' ? +1 : -1);
minb[u] = min(minb[u], bal[u]);
if(bal[u] <= 0 && minb[u] - bal[u] >= 0){
ted[-bal[u]] += dt;
}
for(auto v : adj[u]){
if(v == par || hide[v]) continue;
Upd(v, u, dt);
}
}
void Calc(ll u, ll par, ll b, ll mb){
b = (s[u] == '(' ? +1 : -1) + b;
mb = min(0, (s[u] == '(' ? +1 : -1) + mb);
if(mb >= 0){
ans += ted[b];
if(b == 0) ans ++;
}
for(auto v : adj[u]){
if(v == par || hide[v]) continue;
Calc(v, u, b, mb);
}
}
void DMS(ll u, ll h){
plant(u, -1);
ll cent = CRD(u, -1, (sub[u] + 1) / 2);
globc = cent;
for(auto v : adj[cent]){
if(!hide[v]) Upd(v, cent, +1);
}
for(auto v : adj[cent]){
if(hide[v]) continue;
ll x = (s[cent] == '(' ? +1 : -1);
Upd(v, cent, -1);
Calc(v, cent, x, min(0, x));
Upd(v, cent, +1);
}
if(s[cent] == '(') ans += ted[1];
for(auto v : adj[cent]){
if(!hide[v]) Upd(v, cent, -1);
}
hide[cent] = 1;
for(auto v : adj[cent]){
if(!hide[v]) DMS(v, h + 1);
}
}
int main(){
ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);
cin >> n >> s;
s = "$" + s;
for(int i = 1; i < n; i ++){
ll u, v; cin >> u >> v;
adj[u].push_back(v), adj[v].push_back(u);
}
DMS(1, 0);
cout << ans << '\n';
return 0;
}
/*!
HE'S AN INSTIGATOR,
ENEMY ELIMINATOR,
AND WHEN HE KNOCKS YOU BETTER
YOU BETTER LET HIM IN.
*/
//! N.N
