// #pragma GCC optimize ("O3")
// #pragma GCC optimize ("unroll-loops")
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ldb;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<ldb,ldb> pdd;
#define ff(i,a,b) for(int i = a; i <= b; i++)
#define fb(i,b,a) for(int i = b; i >= a; i--)
#define trav(a,x) for(auto& a : x)
#define sz(a) (int)(a).size()
#define fi first
#define se second
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
// os.order_of_key(k) the number of elements in the os less than k
// *os.find_by_order(k) print the k-th smallest number in os(0-based)
const int mod = 1000000007;
const int inf = 1e9 + 5;
const int mxN = 300005;
int n;
string s;
vector<int> g[mxN];
int cnt[mxN];
bool bio[mxN];
void dfs_cnt(int v, int p){
cnt[v] = 1;
for(auto u : g[v]){
if(u != p && !bio[u]){
dfs_cnt(u, v);
cnt[v] += cnt[u];
}
}
}
int centroid(int v, int p, int vel){
for(auto u : g[v]){
if(u == p || bio[u])continue;
if(cnt[u] > vel / 2)return centroid(u, v, vel);
}
return v;
}
ll br = 0;
int dlA[mxN];
int sumA[mxN];
int grB[mxN];
int sumB[mxN];
int X = 0;
void dfs(int v, int p){
int Y = (s[v] == '(' ? 1 : -1);
sumA[v] = sumA[p] + Y; dlA[v] = min(dlA[p], sumA[v]);
sumB[v] = sumB[p] + Y; grB[v] = min(0, grB[p] + Y);
if(!sumB[v]){
br += (min(0, dlA[v] + X) >= 0) + (grB[v] >= 0);
}
for(auto u : g[v]){
if(u != p && !bio[u]){
dfs(u, v);
}
}
}
vector<int> cuvaj;
int kol[2 * mxN + 5];
void calc(int v, int p){
if(dlA[v] >= sumA[v])br += kol[sumA[v] + mxN];
if(!grB[v])cuvaj.pb(mxN - sumB[v]);
for(auto u : g[v]){
if(u != p && !bio[u]){
calc(u, v);
}
}
}
void decompose(int v){
dfs_cnt(v, -1); int cen = centroid(v, -1, cnt[v]);
bio[cen] = 1; X = (s[cen] == '(' ? 1 : -1);
grB[cen] = min(0, X); sumB[cen] = X;
sumA[cen] = 0; dlA[cen] = 0;
for(auto u : g[cen]){
if(!bio[u]){
dfs(u, cen);
}
}
vector<int> svi;
for(auto u : g[cen]){
if(!bio[u]){
calc(u, cen);
for(auto c : cuvaj){
kol[c] += 1; svi.pb(c);
}
cuvaj.clear();
}
}
for(auto c : svi)kol[c] = 0;
svi.clear();
reverse(all(g[cen]));
for(auto u : g[cen]){
if(!bio[u]){
calc(u, cen);
for(auto c : cuvaj){
kol[c] += 1; svi.pb(c);
}
cuvaj.clear();
}
}
for(auto c : svi)kol[c] = 0;
svi.clear();
for(auto u : g[cen]){
if(!bio[u]){
decompose(u);
}
}
}
int main(){
cin.tie(0)->sync_with_stdio(0);
cin >> n >> s; s = ' ' + s;
ff(i,1,n - 1){
int u, v;
cin >> u >> v;
g[u].pb(v);
g[v].pb(u);
}
decompose(1);
cout << br << '\n';
return 0;
}
/*
4
(())
1 2
2 3
3 4
5
())((
1 2
2 3
2 4
3 5
7
)()()((
1 2
1 3
1 6
2 4
4 5
5 7
// probati bojenje sahovski
*/
