#include <bits/stdc++.h>
#define fi first
#define se second
#define lo long long
#define inf 1000000000
#define md 1000000007
#define li 300005
#define mp make_pair
#define pb push_back
#define pi pair<lo int, int>
using namespace std;
int n, x, y, sz[li], vis[li], mark[li], mark2[li];
char s[li];
int A[li];
lo int ans;
vector<int> v[li], vec, vec2, sil;
int calc(int node, int ata = - 1){
sz[node] = 0;
for(int i = 0; i < (int)v[node].size(); i ++){
int go = v[node][i];
if(go == ata || vis[go] == 1) continue;
sz[node] += calc(go, node);
}
return ++sz[node];
}
int find(int node, int ata , int siz){
for(int i = 0; i < (int)v[node].size(); i ++){
int go = v[node][i];
if(go != ata && vis[go] == 0 && sz[go] > siz / 2)
return find(go , node, siz);
}
return node;
}
void dfs2(int node, int ata, int sm1, int mn1, int sm2, int mn2){
sm1 += A[node];
sm2 -= A[node];
mn1 = min(mn1, sm1);
mn2 = min(mn2, sm2);
if(sm1 <= 0 && sm1 == mn1) ans += 1LL * mark[- sm1];
if(sm2 <= 0 && sm2 == mn2) ans += 1LL * mark2[- sm2];
for(int i = 0; i < (int)v[node].size(); i ++){
int go = v[node][i];
if(go == ata || vis[go] == 1) continue;
dfs2(go, node, sm1, mn1, sm2, mn2);
}
}
void dfs(int node, int ata, int sm1, int mn1, int sm2, int mn2){
sm1 += A[node];
sm2 -= A[node];
mn1 = max(mn1, sm1);
mn2 = max(mn2, sm2);
if(sm1 >= 0 && sm1 == mn1) vec.pb(sm1);
if(sm2 >= 0 && sm2 == mn2) vec2.pb(sm2);
for(int i = 0; i < (int)v[node].size(); i ++){
int go = v[node][i];
if(go == ata || vis[go] == 1) continue;
dfs(go, node, sm1, mn1, sm2, mn2);
}
}
void solve(int cur = 1){
int cen = find(cur , - 1 , calc(cur));
vis[cen] = 1;
for(int i = 0; i < (int)v[cen].size() ; i ++){
int go = v[cen][i];
if(vis[go] == 1) continue;
vec.clear();
vec2.clear();
dfs2(go , - 1, 0 , inf , 0 ,inf);
dfs(go , - 1, 0 , - inf, 0, - inf);
for(int j = 0; j < (int)vec.size(); j ++){
int git = vec[j];
if(git + A[cen] >= 0){
mark[git + A[cen]] ++;
if(git + A[cen] == 0) ans ++;
sil.pb(git + A[cen]);
}
}
for(int j = 0; j < (int)vec2.size() ; j ++){
int git = vec2[j];
if(git - A[cen] >= 0){
mark2[git - A[cen]] ++;
if(git - A[cen] == 0) ans ++;
sil.pb(git - A[cen]);
}
}
}
for(int i = 0; i < (int)sil.size(); i ++){
int go = sil[i];
mark[go] = 0;
mark2[go] = 0;
}
sil.clear();
for(int i = 0; i < (int)v[cen].size(); i ++){
int go = v[cen][i];
if(vis[go] == 0) solve(go);
}
}
int main(){
scanf("%d", &n);
scanf("%s", s + 1);
for(int i = 1; i < n; i ++){
scanf("%d %d", &x ,&y);
v[x].pb(y);
v[y].pb(x);
}
for(int i = 1; i <= n ; i++){
if(s[i] == '(') A[i] = 1;
else A[i] = - 1;
}
solve();
printf("%lld\n", ans);
return 0;
}
