#include <bits/stdc++.h>
using namespace std;
#define fast ios::sync_with_stdio(0);cin.tie(0);
#define s second
#define f first
typedef long long ll;
const ll MOD = 1e9 + 7;
const ll LOGN = 20;
const ll MAXN = 3e5 + 100;
vector<vector<int>> graph;
string s;
int marked[MAXN], sz[MAXN];
map<int,int> cnt;
ll ans = 0;
int get_sz(int node, int parent) {
sz[node] = 1;
for (auto u : graph[node]) {
if (u == parent)
continue;
sz[node] += get_sz(u, node);
}
return sz[node];
}
int find_centro(int node, int parent, int n) {
for (auto u : graph[node]) {
if (u != parent && !marked[u] && sz[u] * 2 >= n)
return find_centro(u, node, n);
}
return node;
}
void dfs(int node, int parent, int sum, int mx, int mn) {
sum += (s[node] == '(' ? 1 : -1);
mx = max(mx, sum);
mn = min(mn, sum);
/*
( ) ) ) (
1 0 -1 -2 -1
sum != mn olduğunda sağlamıyor.
*/
if (sum == mn)
ans += cnt[-mn];
for (auto u : graph[node]) {
if (u == parent || marked[u])
continue;
dfs(u, node, sum, mx, mn);
}
}
void add(int node, int parent, int sum, int mx, int mn) {
sum += (s[node] == '(' ? 1 : -1);
mx = max(mx, sum);
mn = min(mn, sum);
if (sum == mx)
cnt[sum]++;
/*
( ) ) ) ( (
1 0 -1 -2 -1 0
sum = 0
mx = 1
*/
for (auto u : graph[node]) {
if (u == parent || marked[u])
continue;
add(u, node, sum, mx, mn);
}
}
void solve(int node) {
int n = get_sz(node, node);
int centro = find_centro(node, node, n);
cnt.clear();
marked[centro] = true;
if (s[centro] == '(')
cnt[1]++;
for (auto u : graph[centro]) {
if (marked[u])
continue;
dfs(u, centro, 0, 0, 0);
int val = (s[centro] == '(' ? 1 : -1);
add(u, centro, val, max(0, val), min(0, val));
}
ans += cnt[0];
cnt.clear();
reverse(graph[centro].begin(), graph[centro].end());
for (auto u : graph[centro]) {
if (marked[u])
continue;
dfs(u, centro, 0, 0, 0);
int val = (s[centro] == '(' ? 1 : -1);
add(u, centro, val, max(0, val), min(0, val));
}
for (auto u : graph[centro]) {
if (!marked[u])
solve(u);
}
}
int main() {
fast
int n, a, b;
cin >> n >> s;
s = "#" + s;
graph = vector<vector<int>>(n+1, vector<int>());
for (int i = 1; i < n; i++) {
cin >> a >> b;
graph[a].push_back(b);
graph[b].push_back(a);
}
solve(1);
cout << ans << "\n";
}
