#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
template<typename T>
using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define int long long
#define ll long long
#define ar array
#define ld long double
//#define endl '\n'
const ll N = 4e5 + 20;
const ll INF = 1e17;
const int MOD = 1e9 + 7;
int n, A[N], del[N], ans, sz[N];
vector<int> g[N];
map<int,int> cnt;
int dfs1(int x,int p){
sz[x] = 1;
for(auto u : g[x]){
if(u == p || del[u])continue;
sz[x] += dfs1(u, x);
}
return sz[x];
}
int C(int x,int p,int s){
for(auto u: g[x]){
if(u == p || del[u])continue;
if(sz[u] * 2 > s)return C(u, x, s);
}
return x;
}
void dfs2(int x,int p, int sum, int mn,int mx){
sum += A[x];
mx = max(mx, sum);
mn = min(mn, sum);
if(sum <= mn){
ans += cnt[-mn];
}
for(auto u: g[x]){
if(u == p || del[u])continue;
dfs2(u, x, sum, mn, mx);
}
}
void dfs3(int x,int p,int sum, int mn,int mx){
sum += A[x];
mx = max(mx, sum);
mn = min(mn, sum);
if(sum >= mx){
cnt[sum]++;
}
for(auto u: g[x]){
if(u == p || del[u])continue;
dfs3(u, x, sum, mn, mx);
}
}
void cen(int x){
int c = C(x, x, dfs1(x, x));
del[c] = 1;
cnt.clear();
if(A[c] == 1)cnt[A[c]]++;
for(auto u: g[c]){
if(del[u])continue;
dfs2(u, c, 0, 0, 0);
dfs3(u, c, A[c], min(A[c], 0ll), max(A[c], 0ll));
}
ans += cnt[0];
cnt.clear();
reverse(g[c].begin(), g[c].end());
for(auto u: g[c]){
if(del[u])continue;
dfs2(u, c, 0, 0, 0);
dfs3(u, c, A[c], min(A[c], 0ll), max(A[c], 0ll));
}
for(auto u: g[c]){
if(!del[u])cen(u);
}
}
void VladiDadi(){
cin>>n;
string s;
cin>>s;
for(int i = 0;i<n;i++)A[i] = (s[i] == '(' ? 1 : -1);
for(int i =1 ;i<n;i++){
int u, v;
cin>>u>>v;
--u, --v;
g[u].push_back(v);
g[v].push_back(u);
}
cen(0);
cout<<ans;
}
signed main(){
ios::sync_with_stdio(false);
cin.tie(0);
int t = 1;
//cin>>t;
while(t--)
VladiDadi();
}
