#include<bits/stdc++.h>
using namespace std;
int a,b,c,d,e,i,j,ii,jj,zx,xc,bo[300009],cnt,p[300009],pi,msh[300009],dp[300009];
long long pas;
vector <int> v[300009];
int A[300009],Ai,Bi;
pair <int, int> B[300009];
vector <int> vv[300009];
int fx[300009];
string s;
char ch;
void dfs(int q, int w){
pi++;p[pi]=q;
msh[q]=w;
dp[q]=1;
for(vector <int>::iterator it=v[q].begin(); it!=v[q].end(); it++){
if((*it)==w||bo[(*it)]==1) continue;
dfs((*it),q);
dp[q]+=dp[(*it)];
}
}
void dfs2(int q, int w, int rr, int mn){
int RR,MN;
if(s[q]=='('){
RR=rr+1;MN=min(1,mn+1);
}else{
RR=rr-1;MN=min(-1,mn-1);
}
if(MN>=0){
Ai++;A[Ai]=RR;
}
for(vector <int>::iterator it=v[q].begin(); it!=v[q].end(); it++){
if((*it)==w||bo[(*it)]==1) continue;
dfs2((*it),q,RR,MN);
}
}
void dfs3(int q, int w, int rr, int mn, int mn2){
int RR,MN,MN2;
if(s[q]==')'){
RR=rr+1;MN=min(1,mn+1);
MN2=max(mn2,RR);
}else{
RR=rr-1;MN=min(-1,mn-1);
MN2=max(mn2,RR);
}
if(MN>=0){
Bi++;
B[Bi].first=RR;B[Bi].second=MN2;
}
for(vector <int>::iterator it=v[q].begin(); it!=v[q].end(); it++){
if((*it)==w||bo[(*it)]==1) continue;
dfs3((*it),q,RR,MN,MN2);
}
}
long long fun(){
long long sm=0;
for(i=1; i<=Bi; i++){
if(fx[B[i].first]!=cnt){
fx[B[i].first]=cnt;vv[B[i].first].clear();
}
vv[B[i].first].push_back(B[i].second);
}
for(i=1; i<=Bi; i++){
if(i!=1&&B[i-1].first==B[i].first) continue;
sort(vv[B[i].first].begin(),vv[B[i].first].end());
}
for(i=1; i<=Ai; i++){
if(fx[A[i]]!=cnt) continue;
c=lower_bound(vv[A[i]].begin(),vv[A[i]].end(),A[i]+1)-vv[A[i]].begin();
sm+=c;
}
return sm;
}
void dfsa(int q, int w, int rr){
if(s[q]=='('){
rr++;
}else{
rr--;
}
if(rr<0) return;
if(rr==0) pas++;
for(vector <int>::iterator it=v[q].begin(); it!=v[q].end(); it++){
if((*it)==w||bo[(*it)]==1) continue;
dfsa((*it),q,rr);
}
}
void dfsb(int q, int w, int rr){
if(s[q]==')'){
rr++;
}else{
rr--;
}
if(rr<0) return;
if(rr==0) pas++;
for(vector <int>::iterator it=v[q].begin(); it!=v[q].end(); it++){
if((*it)==w||bo[(*it)]==1) continue;
dfsb((*it),q,rr);
}
}
void rec(int q){
pi=0;
dfs(q,0);
int zz=0;
for(int h=1; h<=pi; h++){
bool boo=0;
for(vector <int>::iterator it=v[p[h]].begin(); it!=v[p[h]].end(); it++){
if((*it)==msh[p[h]]||bo[(*it)]==1) continue;
if(dp[(*it)]>pi/2){
boo=1;
break;
}
}
if(pi-dp[p[h]]>pi/2) boo=1;
if(boo==0){
zz=p[h];
break;
}
}
//cout<<q<<" A "<<zz<<endl;
Ai=0;Bi=0;
/*if(s[zz]=='('){
Ai++;
A[Ai]=1;
}*/
for(vector <int>::iterator it=v[zz].begin(); it!=v[zz].end(); it++){
if(bo[(*it)]==1) continue;
if(s[zz]=='('){
dfsa((*it),zz,1);
}else{
dfsb((*it),zz,1);
}
}
//cout<<pas<<endl;
for(vector <int>::iterator it=v[zz].begin(); it!=v[zz].end(); it++){
if(bo[(*it)]==1) continue;
int as=0,sd=0;
if(s[zz]=='('){
as=1;sd=1;
}else{
as=-1;sd=-1;
}
dfs2((*it),zz,as,sd);
dfs3((*it),zz,0,0,0);
}
cnt++;
pas+=fun();
for(vector <int>::iterator it=v[zz].begin(); it!=v[zz].end(); it++){
if(bo[(*it)]==1) continue;
Ai=0;Bi=0;
int as=0,sd=0;
if(s[zz]=='('){
as=1;sd=1;
/*Ai++;
A[Ai]=1;*/
}else{
as=-1;sd=-1;
}
dfs2((*it),zz,as,sd);
dfs3((*it),zz,0,0,0);
cnt++;
pas-=fun();
}
bo[zz]=1;
//cout<<q<<" B "<<zz<<endl;
//cout<<pas<<endl;
for(vector <int>::iterator it=v[zz].begin(); it!=v[zz].end(); it++){
if(bo[(*it)]==1) continue;
rec((*it));
}
//cout<<q<<" C "<<zz<<endl;
}
int main(){
ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0);
//cin>>a;
scanf("%d\n",&a);
/*cin>>s;
s.insert(0,"0");*/
s+="0";
for(i=1; i<=a; i++){
ch=getchar();
s.push_back(ch);
}
for(i=1; i<a; i++){
//cin>>c>>d;
if(i!=a-1) scanf("%d %d\n",&c,&d); else scanf("%d %d",&c,&d);
v[c].push_back(d);
v[d].push_back(c);
}
rec(1);
//cout<<pas;
printf("%llu",pas);
return 0;
}
