#include<bits/stdc++.h>
#define f first
#define s second
#define int long long
using namespace std;
const int N=3e5+5,mod=1e9+7;
int t,ans,sz[N],c[N],fix[N],n,centroid,ans_;
vector<int>V[N];
map<int,int> cnt;
void get_szs(int u,int p){
sz[u] = 1;
for(int i=0;i<V[u].size();i++){
if(V[u][i]==p || fix[V[u][i]]) continue;
get_szs(V[u][i],u);
sz[u] += sz[V[u][i]];
}
}
int find_centroid(int u,int p,int Sz){
for(int i=0;i<V[u].size();i++){
if(V[u][i]==p || fix[V[u][i]]) continue;
if(sz[V[u][i]] >Sz/2) return find_centroid(V[u][i],u,Sz);
}
return u;
}
void half2(int u,int p,int cur,int mn,int x,int y) {
cur += c[u];
x+=(c[u]==1);
mn = min(mn,cur);
y+=(c[u]==-1);
if(y-x >= abs(mn))ans += cnt[y-x];
if(mn+c[centroid] >= 0 && cur+c[centroid] == 0 ) ans_++;
for(int i=0;i<V[u].size();i++){
if(V[u][i] == p || fix[V[u][i]]) continue;
half2(V[u][i],u,cur,mn,x,y);
}
}
void half1(int u,int p,int cur,int mx,int x,int y) {
cur += c[u];
x+=(c[u]==1);
mx = max(mx,cur);
y+=(c[u]==-1);
if(cur-mx >= 0) cnt[x-y]++;
if(cur-mx >= 0 && cur==0) ans_++;
for(int i=0;i<V[u].size();i++) {
if(V[u][i] == p || fix[V[u][i]]) continue;
half1(V[u][i],u,cur,mx,x,y);
}
}
void centroid_decomp(int u){
get_szs(u,0);
int C = find_centroid(u,0,sz[u]);
fix[C] = 1;
centroid=C;
cnt.clear();
ans_ = 0;
for(int i=0;i<V[C].size();i++){
if(fix[V[C][i]]) continue;
half2(V[C][i],C,0,0,0,0);
half1(V[C][i],C,c[C],max(0ll,c[C]),c[C] == 1,c[C]==-1);
}
reverse(V[C].begin(),V[C].end());
cnt.clear();
for(int i=0;i<V[C].size();i++){
if(fix[V[C][i]]) continue;
half2(V[C][i],C,0,0,0,0);
half1(V[C][i],C,c[C],max(0ll,c[C]),c[C] == 1,c[C]==-1);
} ans += ans_/2;
for(int i=0;i<V[C].size();i++){
if(fix[V[C][i]]) continue;
centroid_decomp(V[C][i]);
}
}
main(){
ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0);
cin>>n;
for(int i=1;i<=n;i++){
char ch;
cin>>ch;
if(ch=='(') c[i] = 1;
else c[i] = -1;
}
for(int i=2;i<=n;i++){
int u,v;
cin>>u>>v;
V[u].push_back(v);
V[v].push_back(u);
}
centroid_decomp(1);
cout<<ans;
}
