// Make the best become better
// No room for laziness
#include<bits/stdc++.h>
#define int long long
#define pb push_back
#define fi first
#define se second
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int maxN = 1e6 + 5;
const int mod = 1e9 + 7;
const ll oo = 1e18;
int n;
string s;
vector<int> adj[maxN];
int sz[maxN];
int vis[maxN];
int valid[maxN], valid1[maxN];
pair<int, int> f[maxN], dp[maxN];
int a[maxN];
int res = 0;
int cnt[maxN];
void ReadInput()
{
cin >> n;
cin >> s;
s = ' ' + s;
for(int i=1; i<=n; i++)
a[i] = (s[i] == '(' ? 1 : -1);
for(int i=1; i<n; i++)
{
int u, v;
cin >> u >> v;
adj[u].pb(v);
adj[v].pb(u);
}
}
int dfs(int u, int par)
{
sz[u] = 1;
for(int v : adj[u])
{
if(v == par || vis[v]) continue;
sz[u] += dfs(v, u);
}
return sz[u];
}
int Find_Centroid(int u, int par, int _sz)
{
for(int v : adj[u])
{
if(v == par || vis[v]) continue;
if(sz[v] > _sz / 2) return Find_Centroid(v, u, _sz);
}
return u;
}
void DFS(int u, int par)
{
f[u].fi = f[par].fi + a[u];
f[u].se = max(f[u].fi, f[par].se);
dp[u].fi = f[u].fi;
dp[u].se = min(dp[par].se, dp[u].fi);
valid[u] = f[u].fi >= f[par].se;
valid1[u] = dp[u].fi <= dp[par].se;
if(valid1[u]) cnt[-dp[u].fi]++;
if(valid1[u] && !f[u].fi) res++;
for(int v : adj[u])
{
if(vis[v] || v == par) continue;
DFS(v, u);
}
}
void del(int u, int par)
{
if(valid1[u]) cnt[-dp[u].fi]--;
for(int v : adj[u])
{
if(vis[v] || v == par) continue;
del(v, u);
}
}
int root;
void upd(int u, int par)
{
if(valid[u]) res += cnt[f[u].fi - a[root]];
for(int v : adj[u])
{
if(vis[v] || v == par) continue;
upd(v, u);
}
}
void add(int u, int par)
{
if(valid1[u]) cnt[-dp[u].fi]++;
for(int v : adj[u])
{
if(vis[v] || v == par) continue;
add(v, u);
}
}
void Decompose(int u)
{
root = Find_Centroid(u, 0, dfs(u, 0));
vis[root] = 1;
f[u] = {0, 0};
DFS(root, 0);
for(int v : adj[root])
{
if(vis[v]) continue;
del(v, root);
upd(v, root);
add(v, root);
}
del(root, 0);
for(int v : adj[root])
{
if(vis[v]) continue;
Decompose(v);
}
}
void Solve()
{
Decompose(1);
cout << res;
}
int32_t main()
{
//freopen("sol.inp", "r", stdin);
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
ReadInput();
Solve();
}
