#include <bits/stdc++.h>
//#include<ext/pb_ds/assoc_container.hpp>
//#include<ext/pb_ds/tree_policy.hpp>
using namespace std;
//using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
#define ii pair<int,int>
#define pll pair<ll,ll>
#define vi vector<int>
#define vii vector<ii>
#define vll vector<ll>
#define vpll vector<pll>
#define msi multiset<int>
#define si set<int>
#define PB push_back
#define PF push_front
#define PPB pop_back
#define PPF pop_front
#define X first
#define Y second
#define MP make_pair
#define FOR(i, a, b) for (int i = int(a); i < int(b); i++)
#define REP(i, n) FOR(i, 0, n)
#define all(x) (x).begin(), (x).end()
const int dx[] = {-1, 1, 0, 0};
const int dy[] = {0, 0, -1, 1};
const int dxx[] = {-1, 1, 0, 0, 1, 1, -1, -1};
const int dyy[] = {0, 0, -1, 1, -1, 1, -1, 1};
const int mod = 1e9 + 7;
const int MOD = 1e9 + 7;
const int MAXN = 1e6 + 7;
const int inf = mod;
const ll INF = 1e18;
const int logo = 20;
const int off = 1 << logo;
const int trsz = off << 1;
string s;
int n, sz[MAXN];
bool bio[MAXN];
ll ans = 0;
vi g[MAXN];
map<ii, int> f;
void dfs(int u, int p = -1){
sz[u] = 1;
for(auto &x : g[u]) if(x != p and !bio[x]) dfs(x, u), sz[u] += sz[x];
}
int cen(int u, int p, int szi){
for(auto &x : g[u]) if(x != p and !bio[x]) if(sz[x] * 2 > szi) return cen(x, u, szi);
return u;
}
void dodaj(int x, int t, int a = 0, int b = 0, int p = -1){
if(s[x] == '(') a++;
else{
if(a) a--;
else b++;
}
f[{a, b}] += t;
for(auto &y : g[x]) if(!bio[y] and y != p) dodaj(y, t, a, b, x);
}
void rijesi(int x, int centr, int a = 0, int b = 0, int p = -1){
if(s[x] == ')') b++;
else{
if(b) b--;
else a++;
}
int na = a, nb = b;
if(s[centr] == '(') na++;
else{
if(na) na--;
else nb++;
}
if(nb == 0) ans += (ll)f[{0, na}];
for(auto &y : g[x]) if(!bio[y] and y != p) rijesi(y, centr, a, b, x);
}
void decompose(int u){
dfs(u);
int centr = cen(u, -1, sz[u]);
//sad napravi rjesenje
bio[centr] = 1;
f.clear(); f[{0, 0}] = 1;
for(auto &x : g[centr]) if(!bio[x]) dodaj(x, 1);
if(s[centr] == '(') ans += (ll)f[{0, 1}];
for(auto &x : g[centr]){
if(bio[x]) continue;
dodaj(x, -1);
rijesi(x, centr);
dodaj(x, 1);
}
for(auto &x : g[centr]) if(!bio[x]) decompose(x);
}
void solve(){
cin >> n >> s;
REP(i, n - 1){
int a, b;
cin >> a >> b;
a--, b--;
g[a].PB(b);
g[b].PB(a);
}
dfs(0);
decompose(0);
cout << ans << "\n";
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
int t=1;
//cin >> t;
while(t--)solve();
return 0;
}
