#include <bits/stdc++.h>
#define MAX 300100
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ordered_set tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update>
using namespace std;
int N, S[MAX], sz[MAX];
bool chk[MAX];
ordered_set st[MAX * 2];
vector<int> adj[MAX];
int get_size(int node, int par) {
int res = 1;
for (int i : adj[node]) {
if (i == par || chk[i])
continue;
res += get_size(i, node);
}
return sz[node] = res;
}
int get_centroid(int node, int par, int cap) {
for (int i : adj[node]) {
if (i == par || chk[i])
continue;
if (sz[i] * 2 > cap)
return get_centroid(i, node, cap);
}
return node;
}
void dfs_first(int node, int par, int sum, int mn) {
st[sum + N].insert(mn);
for (int i : adj[node]) {
if (i == par || chk[i])
continue;
dfs_first(i, node, sum + S[i], min(mn, sum + S[i]));
}
}
int dfs(int node, int par, int sum, int mx) {
int res = 0;
if (sum - mx >= 0)
res += st[-sum + N].size() - st[-sum + N].order_of_key(-sum);
for (int i : adj[node]) {
if (i == par || chk[i])
continue;
res += dfs(i, node, sum + S[i], max(mx, sum + S[i]));
}
return res;
}
void clear(int node, int par, int sum, int mn) {
st[sum + N].erase(st[sum + N].find_by_order(st[sum + N].order_of_key(mn)));
for (int i : adj[node]) {
if (i == par || chk[i])
continue;
clear(i, node, sum + S[i], min(mn, sum + S[i]));
}
}
int divide_and_conquer(int node) {
int cent = get_centroid(node, 0, get_size(node, 0));
chk[cent] = true;
int res = 0;
st[S[cent] + N].insert(S[cent]);
for (int i : adj[cent]) {
if (chk[i])
continue;
dfs_first(i, cent, S[cent] + S[i], min(S[cent], S[cent] + S[i]));
}
for (int i : adj[cent]) {
if (chk[i])
continue;
clear(i, cent, S[cent] + S[i], min(S[cent], S[cent] + S[i]));
int X = dfs(i, cent, S[i], max(0, S[i]));
res += X;
dfs_first(i, cent, S[cent] + S[i], min(S[cent], S[cent] + S[i]));
}
res += st[0 + N].size() - st[0 + N].order_of_key(0);
st[S[cent] + N].erase(st[S[cent] + N].find_by_order(st[S[cent] + N].order_of_key(S[cent])));
for (int i : adj[cent]) {
if (chk[i])
continue;
clear(i, cent, S[cent] + S[i], min(S[cent], S[cent] + S[i]));
}
for (int i : adj[cent]) {
if (chk[i])
continue;
res += divide_and_conquer(i);
}
return res;
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0), cout.tie(0);
int U, V;
string T;
cin >> N >> T;
for (int i = 1; i <= N; i++)
S[i] = T[i - 1] == '(' ? 1 : -1;
for (int i = 1; i < N; i++) {
cin >> U >> V;
adj[U].push_back(V), adj[V].push_back(U);
}
cout << divide_and_conquer(1) << '\n';
return 0;
}
