#include<bits/stdc++.h>
using namespace std;
const int mn=3e5+11;
vector<int>adj[mn];
bool r[mn];// removed?
int sz[mn];
int get_tree_size(int u,int par=-1){
sz[u]=1;
for(int v:adj[u])if(v!=par && !r[v])
sz[u]+=get_tree_size(v,u);
return sz[u];
}
int get_centroid(int u,int tree_size,int par=-1){
for(int v:adj[u])if(v!=par && !r[v])
if(sz[v]*2>tree_size)
return get_centroid(v,tree_size,u);
return u;
}
// centroid helper functions
// data processing goes below
inline int get(char x){
return x==')' ? -1 : 1;
}
string a;
struct holder{
int cnt[2*mn];
int elements[3*mn],cc=0;
inline void emplace(int x){
elements[++cc]=x;
cnt[x+mn]++;
}
inline void erase(int x){
if(cnt[x+mn])cnt[x+mn]--;
}
inline int get(int x){
return cnt[x+mn];
}
inline void clear(){
while(cc)erase(elements[cc--]);
}
}st;
void traverse(int u,int par,int cur,int dip,bool dir){
if(dip>=0){
if(dir)st.emplace(cur);
else st.erase(cur);
}
for(int v:adj[u])if(v!=par && !r[v]){
int nxt=cur+get(a[v]);
traverse(v,u,nxt,min(dip+get(a[v]),get(a[v])),dir);
}
}
long long res=0;
void dfs(int u,int par,int cur,int dip){
if(-cur+dip>=0)res+=st.get(-cur);
for(int v:adj[u])if(v!=par && !r[v]){
int nxt=cur+get(a[v]);
dfs(v,u,nxt,min(dip,nxt));
}
}
void centroid_decompose(int root=1){
root=get_centroid(root,get_tree_size(root));
st.clear();
traverse(root,-1,get(a[root]),get(a[root]),1);
for(int other:adj[root])if(!r[other]){
int cur=get(a[root])+get(a[other]);
int dip=min(get(a[other]),cur);
traverse(other,root,cur,dip,0);
dfs(other,root,get(a[other]),get(a[other]));
traverse(other,root,cur,dip,1);
}
res+=st.get(0);
r[root]=true;
for(int other:adj[root])if(!r[other])
centroid_decompose(other);
}
int32_t main()
{
cin.tie(0)->sync_with_stdio(0);
int n;cin>>n;
cin>>a;
a='0'+a;
for(int i=2,u,v;i<=n;i++){
cin>>u>>v;
adj[u].emplace_back(v);
adj[v].emplace_back(u);
}
centroid_decompose();
return cout<<res,0;
}
