#include <bits/stdc++.h>
#pragma GCC optimize ("O2")
#pragma GCC optimize ("unroll-loops")
//#pragma GCC optimize("no-stack-protector,fast-math")
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<pii, int> piii;
typedef pair<ll, ll> pll;
#define debug(x) cerr<<#x<<'='<<(x)<<endl;
#define debugp(x) cerr<<#x<<"= {"<<(x.first)<<", "<<(x.second)<<"}"<<endl;
#define debug2(x, y) cerr<<"{"<<#x<<", "<<#y<<"} = {"<<(x)<<", "<<(y)<<"}"<<endl;
#define debugv(v) {cerr<<#v<<" : ";for (auto x:v) cerr<<x<<' ';cerr<<endl;}
#define all(x) x.begin(), x.end()
#define pb push_back
#define kill(x) return cout<<x<<'\n', 0;
const ld eps=1e-7;
const int inf=1000000010;
const ll INF=10000000000000010LL;
const int mod = 1000000007;
const int MAXN = 300010, LOG=20;
int n, m, k, u, v, x, y, t, a, b;
ll ans;
int A[MAXN];
int sz[MAXN];
bool dead[MAXN];
int cnt[MAXN];
vector<int> G[MAXN];
int dfs1(int node, int par){
sz[node]=1;
for (int v:G[node]) if (v!=par && !dead[v]) sz[node]+=dfs1(v, node);
return sz[node];
}
int Centroid(int node, int par, int n){
for (int v:G[node]) if (v!=par && !dead[v] && 2*sz[v]>n) return Centroid(v, node, n);
return node;
}
void dfs2(int node, int par, int sum, int mn){
mn=min(mn, sum+=A[node]);
//cerr<<"dfs2 "<<node<<" : "<<sum<<' '<<mn<<endl;
if (mn==sum) ans+=cnt[-sum];
for (int v:G[node]) if (!dead[v] && v!=par) dfs2(v, node, sum, mn);
}
void dfs3(int node, int par, int sum, int mn){
sum+=A[node];
mn=min(A[node], mn+A[node]);
mn=min(mn, 0);
if (!mn) cnt[sum]++;
for (int v:G[node]) if (!dead[v] && v!=par) dfs3(v, node, sum, mn);
}
void Decompose(int node){
int root=Centroid(node, node, dfs1(node, node));
dead[root]=1;
fill(cnt, cnt+sz[node]+1, 0);
cnt[0]=1;
for (int v:G[root]) if (!dead[v]){
dfs2(v, root, A[root], min(0, A[root]));
dfs3(v, root, 0, 0);
}
if (A[root]==-1) ans+=cnt[1];
reverse(all(G[root]));
fill(cnt, cnt+sz[node]+1, 0);
for (int v:G[root]) if (!dead[v]){
dfs2(v, root, A[root], min(0, A[root]));
dfs3(v, root, 0, 0);
}
for (int v:G[root]) if (!dead[v]) Decompose(v);
}
int main(){
ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
//freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
cin>>n;
for (int i=1; i<=n; i++){
char ch;
cin>>ch;
A[i]=(ch=='('?+1:-1);
}
for (int i=1; i<n; i++){
cin>>u>>v;
G[u].pb(v);
G[v].pb(u);
}
Decompose(1);
cout<<ans<<'\n';
return 0;
}
