#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/trie_policy.hpp>
// #include <ext/rope>
using namespace std;
// using namespace __gnu_cxx;
// using namespace __gnu_pbds;
void Hollwo_Pelw();
signed main(){
#ifndef hollwo_pelw_local
if (fopen("A.inp", "r"))
assert(freopen("A.inp", "r", stdin)), assert(freopen("A.out", "w", stdout));
#else
auto start = chrono::steady_clock::now();
#endif
cin.tie(0), cout.tie(0) -> sync_with_stdio(0);
int testcases = 1;
// cin >> testcases;
for (int test = 1; test <= testcases; test++){
// cout << "Case #" << test << ": ";
Hollwo_Pelw();
}
#ifdef hollwo_pelw_local
auto end = chrono::steady_clock::now();
cout << "\nExcution time : " << chrono::duration_cast<chrono::milliseconds> (end - start).count() << "[ms]" << endl;
#endif
}
const int N = 3e5 + 5;
int n, a[N];
vector<int> adj[N];
char s[N];
int siz[N], mark[N];
#define for_cen(v, u) for (int v : adj[u]) if (!mark[v])
long long res;
int find_sz(int u, int p) {
siz[u] = 1;
for_cen(v, u) if (v != p)
siz[u] += find_sz(v, u);
return siz[u];
}
int find_cen(int u, int p, const int &tot) {
for_cen(v, u) if (v != p)
if (siz[v] > tot / 2)
return find_cen(v, u, tot);
return u;
}
struct freq_array {
int cnt[N], ver[N], vercnt;
inline void clear() { vercnt ++; }
inline void add(int p, int v) {
// cout << "add " << p << ' ' << v << '\n';
if (p < 0) return ;
if (ver[p] ^ vercnt)
ver[p] = vercnt, cnt[p] = 0;
cnt[p] += v;
}
inline int query(int p) {
if (p < 0) return 0;
if (ver[p] ^ vercnt)
ver[p] = vercnt, cnt[p] = 0;
// cout << "query " << p << ' ' << cnt[p] << '\n';
return cnt[p];
}
} cnt;
int val_up[N], min_up[N];
int val_dw[N], min_dw[N];
void pre_dfs(int u, int p) {
for_cen(v, u) if (v != p) {
val_dw[v] = val_dw[u] + a[v];
min_dw[v] = min(min_dw[u], val_dw[v]);
val_up[v] = val_up[u] + a[v];
min_up[v] = min(0 , min_up[u] + a[v]);
pre_dfs(v, u);
}
}
void dfs_query(int u, int p) {
if (val_dw[u] == min_dw[u]) {
// cout << "u = " << u << " -> ";
res += cnt.query(-val_dw[u]);
}
for_cen(v, u) if (v != p)
dfs_query(v, u);
}
void dfs_update(int u, int p, int w) {
if (min_up[u] >= 0) {
// cout << "u = " << u << " -> ";
cnt.add(val_up[u], w);
}
for_cen(v, u) if (v != p)
dfs_update(v, u, w);
}
void centroid_decomp(int r) {
int tot = find_sz(r, r);
r = find_cen(r, r, tot);
// cout << "SOLVE " << r << ' ' << tot << '\n';
val_up[r] = a[r];
min_up[r] = min(a[r], 0);
val_dw[r] = min_dw[r] = 0;
pre_dfs(r, r);
cnt.clear();
dfs_update(r, r, 1);
dfs_query(r, r);
for_cen(v, r) {
cnt.clear();
dfs_update(v, r, -1);
dfs_query(v, r);
}
mark[r] = 1;
for_cen(v, r)
centroid_decomp(v);
}
void Hollwo_Pelw(){
cin >> n >> (s + 1);
for (int i = 1; i <= n; i++)
a[i] = s[i] == '(' ? 1 : -1;
for (int i = 1, u, v; i < n; i++) {
cin >> u >> v;
adj[u].push_back(v);
adj[v].push_back(u);
}
centroid_decomp(1);
cout << res << '\n';
}
