#include <bits/stdc++.h>
#define F first
#define S second
#define pb push_back
#define N 300010
using namespace std;
typedef long long ll;
map<int,int> mp;
vector <int> g[N];
int sz[N], n, bl[N], need[N], res[N];
ll ans = 0;
bool mk[N];
string s;
void dfs(int v, int p)
{
sz[v] = 1;
for (auto it : g[v])
{
if (it == p || mk[it]) continue;
dfs(it, v);
sz[v] += sz[it];
}
}
int fnd_cent(int v, int p)
{
if (p != -1) {sz[p] -= sz[v]; sz[v] += sz[p];}
for (auto it : g[v])
if (!mk[it] && sz[it] + sz[it] > sz[v]) return fnd_cent(it, v);
return v;
}
void rec(int v, int p, bool f)
{
if (need[v] == abs(bl[v]) && bl[v] <= 0 && res[v] == 0) mp[abs(bl[v])]++;
if (!f && bl[v] == 0 && need[v] == 0 && res[v] == 0) ans++;
for (auto it : g[v])
{
if (mk[it] || it == p) continue;
if (!f)
{
bl[it] = bl[v];
need[it] = need[v];
res[it] = res[v];
if (s[it] == '(') {res[it]++; bl[it]++;}
else {bl[it]--; if (res[it] > 0) res[it]--; else need[it]++;}
}
rec(it, v, f);
}
}
void dec(int v, int p)
{
if (need[v] == abs(bl[v]) && bl[v] <= 0 && res[v] == 0) mp[abs(bl[v])]--;
for (auto it : g[v])
{
if (mk[it] || it == p) continue;
dec(it, v);
}
}
void dfser(int v, int p, int need, int b)
{
if (s[v] == '(') {b++; need--; need = max(need, 0);}
else {need++; b--;}
if (b >= 0 && need == 0) ans += ll(mp[b]);
for (auto it : g[v])
{
if (mk[it] || it == p) continue;
dfser(it, v, need, b);
}
}
void calc(int v)
{
mp.clear();
mk[v] = 1;
bl[v] = need[v] = res[v] = 0;
if (s[v] == '(') {res[v]++; bl[v]++;}
else {bl[v]--; need[v] = 1;}
rec(v, -1, 0);
for (auto it : g[v])
{
if (mk[it]) continue;
dec(it, -1);
dfser(it, -1, 0, 0);
rec(it, -1, 1);
}
for (auto it : g[v])
{
if (mk[it]) continue;
int root = fnd_cent(it, -1);
if (root != -1)
{
dfs(root, -1);
calc(root);
}
}
}
int main()
{
ios_base::sync_with_stdio(0); istream::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n;
cin >> s;
for (int i = 1; i < n; i++)
{
int x, y;
cin >> x >> y;
x--; y--;
g[x].pb(y);
g[y].pb(x);
}
dfs(0, -1);
int root = fnd_cent(0, -1);
dfs(root, -1);
calc(root);
cout << ans << endl;
}
