#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define all(v) v.begin(), v.end()
typedef long long ll;
typedef vector<int> vi;
const int maxn = 3e5 + 7;
int n, c, it, val[maxn], sz[maxn], d[maxn], mf[maxn], mb[maxn], cnt[2 * maxn];
ll add, ans;
bool vis[maxn];
string s;
vi g[maxn];
void dfs1(int v, int p){
sz[v] = 1;
d[v] = d[p] + val[v];
mb[v] = min(0, val[v] + min(mb[p], 0));
mf[v] = min(mf[p], d[v]);
for (int ne : g[v]){
if (vis[ne] || ne == p)
continue;
dfs1(ne, v);
sz[v] += sz[ne];
}
}
int cen(int v, int p){
bool b = 1;
for (int ne : g[v]){
if (vis[ne])
continue;
if (sz[ne] > sz[v] / 2)
b = 0;
}
if (b)
return v;
for (int ch : g[v]){
if (ch == p || vis[ch])
continue;
sz[v] -= sz[ch];
sz[ch] += sz[v];
int ret = cen(ch, v);
if (ret != -1)
return ret;
sz[ch] -= sz[v];
sz[v] += sz[ch];
}
return -1;
}
void dfs2(int v, int p, bool b){
int db = d[v] - val[c];
if (b){
add += (mf[v] >= db) * cnt[sz[c] - db];
if (it == 0){
add += (d[v] == 0 && mb[v] == 0);
add += (d[v] == 0 && mf[v] == 0);
}
} else if (min(d[v], mb[v]) >= 0)
cnt[sz[c] + d[v]]++;
for (int ch : g[v]){
if (ch == p || vis[ch])
continue;
dfs2(ch, v, b);
}
}
void rek(int v){
c = -1;
dfs1(v, 0);
c = cen(v, 0);
dfs1(c, 0);
add = 0;
for (it = 0; it < 2; it++){
for (int i = 0; i <= 2 * sz[c]; i++)
cnt[i] = 0;
for (int ch : g[c]){
if (vis[ch])
continue;
dfs2(ch, c, 1);
dfs2(ch, c, 0);
}
reverse(all(g[c]));
}
ans += add;
vis[c] = 1;
for (int ch : g[c]){
if (vis[ch])
continue;
rek(ch);
}
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> n >> s;
s = '.' + s;
for (int i = 1; i < n; i++){
int u, v;
cin >> u >> v;
g[u].pb(v);
g[v].pb(u);
}
for (int i = 1; i <= n; i++){
if (s[i] == '(')
val[i] = 1;
else
val[i] = -1;
}
rek(1);
cout << ans << "\n";
return 0;
}
