#include<bits/stdc++.h>
using namespace std;
#define LL long long
#define X first
#define Y second
#define PB push_back
#define INS insert
#define pii pair<int,int>
const int N = 3e5;
const int INF = 1e9;
const int MOD = 1e9+7;
vector<int>v[N];
int sz[N];
int flg[N];
int rj;
string s;
map<pair<int,pii>,int>map2;
vector<pair<int,pii>>rlb;
void dfs(int tr,int pr=-1) {
for (int i=0;i<v[tr].size();i++) {
if (v[tr][i]==pr or flg[v[tr][i]]==1) continue;
dfs(v[tr][i],tr);
sz[tr]+=sz[v[tr][i]];
}
sz[tr]++;
}
int fnd_cnt(int tr,int n,int pr = -1) {
for (int i=0;i<v[tr].size();i++) {
if (v[tr][i]==pr or flg[v[tr][i]]==1) continue;
if (sz[v[tr][i]]*2>n) return fnd_cnt(v[tr][i],n,tr);
}
return tr;
}
pii br3;
void dfs2(int tr,pii br,pii br2,int pr = -1) {
if (s[tr]=='(') br.X++;
else {
if (br.X>0) br.X--;
else br.Y++;
}
// drugi
if (s[tr]==')') br2.Y++;
else {
if (br2.Y>0) br2.Y--;
else br2.X++;
}
if (s[tr]==')') br3.Y++;
else {
if (br3.Y>0) br3.Y--;
else br3.X++;
}
if (br.X==0) rj+=map2[{2,{br.Y,br.X}}];
if (br2.Y==0) rj+=map2[{1,{br2.Y,br2.X}}];
if (br3.X==0 and br3.Y==0) rj++;
//cout <<tr<<" :: "<<br.X<<" "<<br.Y<< " :: "<<br2.X<<" "<<br2.Y<<" >. "<<br3.X<<" "<<br3.Y<<endl;
//cout << map2[{2,{br.Y,br.X}}]<<" + "<<map2[{1,{br2.Y,br2.X}}]<<endl;
rlb.PB({1,br});
rlb.PB({2,br2});
for (int i=0;i<v[tr].size();i++) {
if (v[tr][i]==pr or flg[v[tr][i]]==1) continue;
dfs2(v[tr][i],br,br2,tr);
}
}
void cnt(int tr) {
dfs(tr);
if (sz[tr]==1) return;
int tr2=fnd_cnt(tr,sz[tr]);
flg[tr2]=1;
// izracunaj start
//cout <<tr2<<"START"<<endl;
map2.clear();
pii aa = {0,0};
if (s[tr2]=='(') aa.X++;
else aa.Y++;
map2[{2,{0,0}}]=1;
for (int i=0;i<v[tr2].size();i++) {
if (flg[v[tr2][i]]==1) continue;
br3=aa;
dfs2(v[tr2][i],aa,{0,0});
//cout<<"NOVO"<<endl;
while (!rlb.empty()) {
map2[rlb.back()]++;
rlb.pop_back();
}
}
//rj+=map2[{2,{aa.Y,aa.X}}];
//cout << map2[{2,{aa.Y,aa.X}}]<< " DODANO "<<endl;
// izracunaj end
for (int i=0;i<v[tr2].size();i++) {
if (flg[v[tr2][i]]) continue;
cnt(v[tr2][i]);
}
}
void solve() {
int n,a,b;
cin>>n;
cin>>s;
s='0'+s;
for (int i=0;i<n-1;i++) {
int a,b;
cin>>a>>b;
v[a].PB(b);
v[b].PB(a);
}
cnt(1);
cout << rj;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
solve();
}
