#include <bits/stdc++.h>
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define pb push_back
#define FIO ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
using namespace std;
typedef long long ll;
typedef pair <ll, ll> pii;
const int N = 3e5 + 7;
int n;
ll res;
string a;
vector <int> adj[N];
int off[N], ofg[N], siz[N];
map <int, int> f[N], g[N];
void pdfs(int x, int p = -1) {
siz[x] = 1;
for (int y : adj[x]) {
if (y == p) continue;
pdfs(y, x);
siz[x] += siz[y];
}
}
void dfs(int x) {
for (int y : adj[x]) dfs(y);
if (adj[x].empty()) {
if (a[x] == '(') f[x][1] = 1;
else g[x][1] = 1;
return;
}
swap(off[x], off[adj[x][0]]);
swap(ofg[x], ofg[adj[x][0]]);
swap(f[x], f[adj[x][0]]);
swap(g[x], g[adj[x][0]]);
int o = 2*(a[x] == '(')-1;
for (int i = 1; i < adj[x].size(); i++) {
int y = adj[x][i];
for (auto z : f[y]) if (g[x].find(z.F+off[y]-ofg[x]+o) != g[x].end()) res += (ll)g[x][z.F+off[y]-ofg[x]+o]*z.S;
for (auto z : g[y]) if (f[x].find(z.F+ofg[y]-off[x]-o) != f[x].end()) res += (ll)f[x][z.F+ofg[y]-off[x]-o]*z.S;
for (auto z : f[y]) f[x][z.F+off[y]-off[x]] += z.S;
for (auto z : g[y]) g[x][z.F+ofg[y]-ofg[x]] += z.S;
}
if (a[x] == '(') {
f[x][-off[x]]++;
if (g[x].find(-ofg[x]) != g[x].end()) g[x].erase(-ofg[x]);
off[x]++;
ofg[x]--;
}
else {
g[x][-ofg[x]]++;
if (f[x].find(-off[x]) != f[x].end()) f[x].erase(-off[x]);
off[x]--;
ofg[x]++;
}
if (f[x].find(-off[x]) != f[x].end()) res += f[x][-off[x]];
if (g[x].find(-ofg[x]) != g[x].end()) res += g[x][-ofg[x]];
}
int main () {
FIO;
cin >> n >> a;
for (int i = 1; i < n; i++) {
int x, y; cin >> x >> y; x--; y--;
adj[x].pb(y);
adj[y].pb(x);
}
pdfs(0);
for (int i = 0; i < n; i++) {
sort(all(adj[i]), [&](int x, int y){return siz[x] < siz[y];});
if (i) adj[i].pop_back();
reverse(all(adj[i]));
}
dfs(0);
cout << res << "\n";
return 0;
}
