#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
#define ll long long
#define F first
#define S second
#define pb push_back
const int N = 3e5 + 10;
const int LOG = 25;
const int MOD = 1e9 + 7;
const ll inf = 1e9 + 5;
int n, m;
vector <int> g[N];
int a[N];
string s;
int sz[N];
bool dead[N];
ll cnt[N];
void dfs(int v, int p){
sz[v] = 1;
for (int u : g[v]){
if (u == p || dead[u]) continue;
dfs(u, v);
sz[v] += sz[u];
}
return;
}
int find_centr(int v, int p, int root){
for (int u : g[v]){
if (u == p || dead[u]) continue;
if (sz[root] < 2 * sz[u]){
return find_centr(u, v, root);
}
}
return v;
}
void add(int v, int p, int op, int cl){
if (a[v] == 1){
if (cl) cl --;
else op ++;
}
if (a[v] == -1) cl ++;
if (cl == 0) cnt[op] ++;
for (int u : g[v]){
if (u == p || dead[u]) continue;
add(u, v, op, cl);
}
return;
}
ll find_ans(int v, int p, int op, int cl){
ll ret = 0;
if (a[v] == 1) op ++;
if (a[v] == -1){
if (op) op --;
else cl ++;
}
if (op == 0){
ret += cnt[cl] + (cl == 0);
}
for (int u : g[v]){
if (u == p || dead[u]) continue;
ret += find_ans(u, v, op, cl);
}
return ret;
}
void del(int v, int p, int op, int cl){
if (a[v] == 1){
if (cl) cl --;
else op ++;
}
if (a[v] == -1) cl ++;
if (cl == 0) cnt[op] --;
for (int u : g[v]){
if (u == p || dead[u]) continue;
del(u, v, op, cl);
}
return;
}
ll oth(int v, int p, int op, int cl){
ll ret = 0;
if (a[v] == 1){
if (cl) cl --;
else op ++;
}
if (a[v] == -1) cl ++;
if (op == 0 && cl == 0) ret ++;
for (int u : g[v]){
if (u == p || dead[u]) continue;
ret += oth(u, v, op, cl);
}
return ret;
}
ll solve(int v){
dfs(v, 0);
v = find_centr(v, 0, v);
dead[v] = 1;
ll ret = 0;
for (int u : g[v]){
if (dead[u]) continue;
add(u, v, 0, 0);
}
for (int u : g[v]){
if (dead[u]) continue;
del(u, v, 0, 0);
ll res = find_ans(u, v, (a[v] == 1), (a[v] == -1));
ret += res + oth(u, v, (a[v] == 1), (a[v] == -1));
add(u, v, 0, 0);
}
for (int u : g[v]){
if (dead[u]) continue;
del(u, v, 0, 0);
}
for (int u : g[v]){
if (!dead[u]){
ret += solve(u);
}
}
return ret;
}
int main() {
ios_base::sync_with_stdio(0),cin.tie(0);cout.tie(0);
cin >> n >> s;
s = ' ' + s;
for (int i = 1; i <= n; i ++){
a[i] = ((s[i] == '(') ? 1 : -1);
}
for (int i = 0; i < n - 1; i ++){
int u, v;
cin >> u >> v;
g[u].pb(v); g[v].pb(u);
}
cout << solve(1) << '\n';
return 0;
}
