#include<bits/stdc++.h>
using namespace std;
#define LL long long
#define int LL
#define X first
#define Y second
#define PB push_back
#define INS insert
#define pii pair<int,int>
const int N = 6e5;
const int INF = 1e9;
const int MOD = 1e9+7;
vector<int>v[N];
vector<int>rb;
int sz[N];
int flg[N];
int rj;
string s;
int put[N];
void dfs(int tr,int pr=-1) {
sz[tr]=0;
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;
}
int zbroji(char a) {
if (a=='(') return 1;
else return -1;
}
void umi(int tr,int pr,bool cnt,int br,int brm,int md) {
br+=zbroji(s[tr]);
brm+=zbroji(s[tr]);
brm=min(0ll,brm);
md=min(md,br);
if (cnt and br<=0 and br==md) {
rj += put[-br];
}
else if (brm>=0 and br>=0) put[br]++;
for (int i=0;i<v[tr].size();i++) {
if (flg[v[tr][i]]==1 or pr==v[tr][i]) continue;
umi(v[tr][i],tr,cnt,br,brm,md);
}
}
void cnt(int tr) {
dfs(tr);
int tr2=fnd_cnt(tr,sz[tr]);
flg[tr2]=1;
put[0]++;
for (int i=0;i<v[tr2].size();i++) {
if (flg[v[tr2][i]]==1) continue;
umi(v[tr2][i],tr2,true,zbroji(s[tr2]),zbroji(s[tr2]),zbroji(s[tr2]));
umi(v[tr2][i],tr2,false,0,0,0);
}
if (zbroji(s[tr2]) < 0) rj+=put[-zbroji(s[tr2])];
for (int i=0;i<sz[tr]+1000;i++) put[i]=0;
reverse(v[tr2].begin(),v[tr2].end());
for (int i=0;i<v[tr2].size();i++) {
if (flg[v[tr2][i]]==1) continue;
umi(v[tr2][i],tr2,true,zbroji(s[tr2]),zbroji(s[tr2]),zbroji(s[tr2]));
umi(v[tr2][i],tr2,false,0,0,0);
}
for (int i=0;i<sz[tr]+1000;i++) put[i]=0;
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;
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0);
solve();
}
