#include <bits/stdc++.h>
#define pb push_back
#define fr first
#define se second
using namespace std;
typedef long long int ll;
typedef pair<int, int> pii;
typedef vector <int> vi;
const int maxn=2*1e5+5;
int bio[maxn], sz[maxn], z[maxn];
vi graf[maxn];
void DFS (int cvor, int parent = -1) {
sz[cvor] = 1;
for (int i = 0; i < graf[cvor].size(); i++) {
if (graf[cvor][i] == parent || bio[graf[cvor][i]]) continue;
DFS (graf[cvor][i], cvor); sz[cvor] += sz[graf[cvor][i]];
}
}
int findcen (int cvor, int vel, int parent = -1) {
for (int i = 0; i < graf[cvor].size(); i++) {
if (graf[cvor][i] == parent || bio[graf[cvor][i]]) continue;
if (sz[graf[cvor][i]] * 2 > vel) return findcen (graf[cvor][i], vel, cvor);
}
bio[cvor] = 1;
return cvor;
}
ll ans = 0;
map <pii, ll> f;
void DFSadd (int cvor, int predznak, pii add, int parent = -1) {
if (z[cvor]) add.fr++;
else if (add.fr > 0) add.fr--;
else add.se++;
for (int i = 0; i < graf[cvor].size(); i++) {
if (graf[cvor][i] == parent || bio[graf[cvor][i]]) continue;
DFSadd (graf[cvor][i], predznak, add, cvor);
}
if (predznak == 1) {
if (f.find(add) == f.end()) f[add] = 1;
else f[add]++;
}
else f[add]--;
}
void DFScount (int cvor, pii add, int parent = -1) {
if (z[cvor] && add.se > 0) add.se--;
else if (z[cvor]) add.fr++;
else add.se++;
for (int i = 0; i < graf[cvor].size(); i++) {
if (graf[cvor][i] == parent || bio[graf[cvor][i]]) continue;
DFScount (graf[cvor][i], add, cvor);
}
if (add.se == 0 && f.find({0, add.fr}) != f.end())
ans += f[{0, add.fr}];
}
void solve (int cvor) {
DFS (cvor);
int centroid = findcen (cvor, sz[cvor]);
pii p = {0, 1};
if (z[centroid]) p = {1, 0};
for (int i = 0; i < graf[centroid].size(); i++) {
if (bio[graf[centroid][i]]) continue;
DFSadd (graf[centroid][i], 1, p);
}
if (f.find(p) == f.end()) f[p] = 1;
else f[p]++;
ans += f[{0, 0}];
for (int i = 0; i < graf[centroid].size(); i++) {
if (bio[graf[centroid][i]]) continue;
DFSadd (graf[centroid][i], -1, p);
DFScount (graf[centroid][i], {0, 0});
DFSadd (graf[centroid][i], 1, p);
}
for (int i = 0; i < graf[centroid].size(); i++) {
if (bio[graf[centroid][i]]) continue;
f.clear();
solve (graf[centroid][i]);
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n, a, b;
cin >> n;
char c;
for (int i = 0; i < n; i++) {
cin >> c;
if (c == '(') z[i] = 1;
}
for (int i = 0; i < n-1; i++) {
cin >> a >> b;
a--; b--;
graf[a].pb(b);
graf[b].pb(a);
}
solve (0);
cout << ans << endl;
return 0;
}
