#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define endl '\n'
#define fi first
#define se second
#define For(i, l, r) for (auto i = l; i < r; i++)
#define ForE(i, l, r) for (auto i = l; i <= r; i++)
#define FordE(i, l, r) for (auto i = l; i >= r; i--)
#define Fora(v, a) for (auto v: a)
#define bend(a) a.begin(), a.end()
#define isz(a) ((signed)a.size())
using ll = long long;
using ld = long double;
using pii = pair <int, int>;
using vi = vector <int>;
using vpii = vector <pair <int, int>>;
using vvi = vector <vector <int>>;
template <class T>
using ordered_multiset = tree <T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
const int N = 3e5 + 5;
int n;
string s; int val[N];
vi adj[N];
int par[N], sz[N];
int ctall;
vi adjct[N];
int parct[N], hct[N];
bool block[N];
void dfs_cpn_ct(int u){
sz[u] = 1;
Fora(v, adj[u]){
if (v == par[u] or block[v]){
continue;
}
par[v] = u;
dfs_cpn_ct(v);
sz[u] += sz[v];
}
}
int dfs_ct(int u){
par[u] = 0;
dfs_cpn_ct(u);
if (sz[u] == 1){
return u;
}
int sz_cpn = sz[u];
while (1){
int v = 0;
Fora(tv, adj[u]){
if (tv == par[u] or block[tv]){
continue;
}
if (sz[tv] * 2 > sz_cpn){
v = tv;
break;
}
}
if (v == 0){
break;
}
u = v;
}
block[u] = 1;
Fora(v, adj[u]){
if (block[v]){
continue;
}
v = dfs_ct(v);
adjct[u].emplace_back(v);
parct[v] = u;
}
return u;
}
ll ans;
void dfs_cpn_bracket_count(int u, int sum, int mnprefup, int mnprefdown, ordered_multiset <int> &mtsup, ordered_multiset <int> &mtsdown){
if (sum >= 0 and mnprefup >= 0){
ans += mtsdown.order_of_key(sum + 1) - mtsdown.order_of_key(sum);
}
if (sum <= 0 and mnprefdown == sum){
ans += mtsup.order_of_key(-sum + 1) - mtsup.order_of_key(-sum);
}
Fora(v, adj[u]){
if (v == par[u] or block[v]){
continue;
}
par[v] = u;
dfs_cpn_bracket_count(v, sum + val[v], min(val[v], mnprefup + val[v]), min(mnprefdown, sum + val[v]), mtsup, mtsdown);
}
}
void dfs_cpn_bracket_insert(int u, int sum, int mnprefup, int mnprefdown, ordered_multiset <int> &mtsup, ordered_multiset <int> &mtsdown){
if (sum >= 0 and mnprefup >= 0){
mtsup.insert(sum);
}
if (sum <= 0 and mnprefdown == sum){
mtsdown.insert(-sum);
}
Fora(v, adj[u]){
if (v == par[u] or block[v]){
continue;
}
par[v] = u;
dfs_cpn_bracket_insert(v, sum + val[v], min(val[v], mnprefup + val[v]), min(mnprefdown, sum + val[v]), mtsup, mtsdown);
}
}
void dfs_bracket(int u){
ordered_multiset <int> mtsup, mtsdown;
if (val[u] == 1){
mtsup.insert(1);
}
else{
mtsdown.insert(1);
}
par[u] = 0;
Fora(v, adj[u]){
if (block[v]){
continue;
}
par[v] = u;
dfs_cpn_bracket_count(v, val[v], min(val[v], 0), min(val[v], 0), mtsup, mtsdown);
dfs_cpn_bracket_insert(v, val[u] + val[v], min({0, val[v], val[v] + val[u]}), min({0, val[u], val[u] + val[v]}), mtsup, mtsdown);
}
block[u] = 1;
Fora(v, adjct[u]){
dfs_bracket(v);
}
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
// freopen("KEK.inp", "r", stdin);
// freopen("KEK.out", "w", stdout);
cin >> n;
cin >> s; s = ' ' + s;
For(i, 1, n){
int u, v; cin >> u >> v;
adj[u].emplace_back(v); adj[v].emplace_back(u);
}
ForE(i, 1, n){
val[i] = (s[i] == '(' ? 1 : -1);
}
ctall = dfs_ct(1);
memset(block, 0, sizeof(block));
dfs_bracket(ctall);
cout << ans << endl;
}
/*
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INPUT: |
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OUTPUT: |
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==================================================+
*/
