#include <bits/stdc++.h>
using namespace std;
#define LL long long
#define int LL
#define PB push_back
const int N = 6e5 + 5;
vector<int> v[N];
int sz[N];
bool flg[N];
string s;
int put[N];
long long rj = 0;
vector<int> touched;
int zbroji(char a) {
return (a == '(' ? 1 : -1);
}
void dfs(int tr, int pr = -1) {
sz[tr] = 1;
for (int nx : v[tr]) {
if (nx == pr || flg[nx]) continue;
dfs(nx, tr);
sz[tr] += sz[nx];
}
}
int fnd_cnt(int tr, int n, int pr = -1) {
for (int nx : v[tr]) {
if (nx == pr || flg[nx]) continue;
if (sz[nx] * 2 > n)
return fnd_cnt(nx, n, tr);
}
return tr;
}
void umi(int tr, int pr, bool cnt, int br, int brm, int md) {
br += zbroji(s[tr]);
brm += zbroji(s[tr]);
brm = min(0LL, brm);
md = min(md, br);
if (cnt) {
if (br <= 0 && br == md) {
if (-br < N) rj += put[-br];
}
} else {
if (brm >= 0 && br >= 0) {
if (put[br] == 0) touched.PB(br);
put[br]++;
}
}
for (int nx : v[tr]) {
if (nx == pr || flg[nx]) continue;
umi(nx, tr, cnt, br, brm, md);
}
}
void clear_put() {
for (int x : touched) put[x] = 0;
touched.clear();
}
void cnt(int tr) {
dfs(tr);
int c = fnd_cnt(tr, sz[tr]);
flg[c] = true;
int delta = zbroji(s[c]);
put[0] = 1;
touched.PB(0);
for (int nx : v[c]) {
if (flg[nx]) continue;
umi(nx, c, true, delta, delta, delta);
umi(nx, c, false, 0, 0, 0);
}
if (delta < 0 && -delta < N) rj += put[-delta];
clear_put();
reverse(v[c].begin(), v[c].end());
put[0] = 1;
touched.PB(0);
for (int nx : v[c]) {
if (flg[nx]) continue;
umi(nx, c, true, delta, delta, delta);
umi(nx, c, false, 0, 0, 0);
}
clear_put();
for (int nx : v[c]) {
if (!flg[nx]) cnt(nx);
}
}
void solve() {
int n;
cin >> n;
cin >> s;
s = ' ' + s;
for (int i = 0; i < n - 1; i++) {
int a, b;
cin >> a >> b;
v[a].PB(b);
v[b].PB(a);
}
cnt(1);
cout << rj << '\n';
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
}
