#include <bits/stdc++.h>
using namespace std;
#define int long long
long long sz[300007];long long all = 0;
long long vis[300007];
vector<int> adj[300007];
int ss = 0;
long long zz[300007];
string s;
long long c = 0;
void calc(int no,int pr,int ch,int bra){
if(ss==0){
if(s[no-1]=='('){bra++;ch--;ch=max(ch,0LL);}
if(s[no-1]==')'){bra--;ch++;}
if(bra>=0&&ch==0)zz[bra]++;
}else if(ss==1){
if(s[no-1]=='('){bra++;ch++;}
if(s[no-1]==')'){bra--;ch--;ch=max(ch,0LL);}
if(bra<=0&&ch==0){
all+=zz[-bra];
}
//if(bra==0&&ch==0)c++;
}else{
if(s[no-1]=='('){bra++;ch--;ch=max(ch,0LL);}
if(s[no-1]==')'){bra--;ch++;}
if(bra>=0&&ch==0)zz[bra]--;
}
for(auto i:adj[no]){
if(i==pr||vis[i])continue;
calc(i,no,ch,bra);
}
}
int dfs(int no,int pr){
sz[no] = 1;
for(auto i:adj[no]){
if(i==pr||vis[i]!=0)continue;
sz[no]+=dfs(i,no);
}
return sz[no];
}
int get_centroid(int no,int ss,int pr){
for(auto i:adj[no]){
if(pr==i||vis[i]!=0)continue;
if(sz[i]*2>ss){
return get_centroid(i,ss,no);
}
}
return no;
}
void centroid(int no){
int cen = get_centroid(no,dfs(no,-1),-1);
for(int i = 0;i<=max(1000LL,sz[cen]+5);i++){
zz[i] = 0;
}
zz[0] = 1;
vis[cen] = 1;
for(auto i:adj[cen]){
if(vis[i])continue;
ss= 0;
calc(i,-1,0,0);
}
if(s[cen-1]==')')all+=zz[1];
for(auto i:adj[cen]){
if(vis[i])continue;
ss = 2;
calc(i,-1,0,0);
ss = 1;
calc(i,-1,(s[cen-1]=='('?1:0),(s[cen-1]=='('?1:-1));
//cout<<all<<" "<<i<<endl;
ss = 0;
calc(i,-1,0,0);
}
for(auto i:adj[cen]){
if(vis[i])continue;
centroid(i);
}
}
signed main(){
ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
int n;
cin>>n>>s;
for(int i = 0;i<n-1;i++){
int a,b;
cin>>a>>b;
adj[a].push_back(b);
adj[b].push_back(a);
}
centroid(1);
cout<<all<<endl;
}
