#include<iostream>
#include<cstring>
#include<vector>
#include<array>
#include<map>
using namespace std;
using LL = long long;
const int maxn = 1e5 + 5;
vector<int> g[maxn];
int a[maxn];
bool v[maxn];

int get_wc(int u, int fa, int tot, int &wc){
    if (v[u]) return 0;
    int mx = 0, sum = 1;
    for(auto j : g[u]){
        if (j == fa) continue;
        int t = get_wc(j, u, tot, wc);
        mx = max(mx, t);
        sum += t;
    }
    mx = max(mx, tot - sum);
    if (mx * 2 <= tot){
        wc = u;
    }
    return sum;
}

int get_sz(int u, int fa){
    if (v[u]) return 0;
    int ans = 1;
    for(auto j : g[u]){
        if (j == fa) continue;
        ans += get_sz(j, u);
    }
    return ans;
}

void dfs(int u, int fa, int sum, int mn, int mx, vector<array<int, 3> > &p){
    if (v[u]) return;
    sum += a[u];
    mn = min(mn, sum);
    mx = max(mx, sum);
    p.push_back({sum, mn, mx});
    for(auto j : g[u]){
        if (j == fa or v[j]) continue;
        dfs(j, u, sum, mn, mx, p);
    }
}

LL ans;

void calc(int u){
    if (v[u]) return;
    get_wc(u, -1, get_sz(u, -1), u);
    v[u] = true;

    map<int, int> mp1;
    vector<map<int, int> > mp2(g[u].size());
    vector<vector<array<int, 3> > > p(g[u].size());
    for(int i = 0; i < g[u].size(); i++){
        int j = g[u][i];
        dfs(j, -1, 0, 0, 0, p[i]);
        for(auto [sum, mn, mx] : p[i]){
            if (sum + a[u] == 0){
                if (min(mn + a[u], a[u]) >= 0) ans += 1;
                if (min(sum - mx, sum + a[u]) >= 0) ans += 1;
            }
            int need = 0 - (sum + a[u]);
            if (need >= 0 and need + a[u] >= 0 and need + a[u] + mn >= 0){
                mp1[sum] += 1;
                mp2[i][sum] += 1;
            }
        }
    }
    for(int i = 0; i < g[u].size(); i++){
        for(auto [sum, mn, mx] : p[i]){
            if (min(sum - mx, sum + a[u]) < 0) continue;
            int need = 0 - (sum + a[u]);
            if (mp1.contains(need)) ans += mp1[need];
            if (mp2[i].contains(need)) ans -= mp2[i][need];
        }
    }

    for(auto j : g[u]){
        calc(j);
    }
}

int main(){

#ifdef LOCAL
    freopen("data.in", "r", stdin);
    freopen("data.out", "w", stdout);
#endif

    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(0);

    int n;
    cin >> n;
    string str;
    cin >> str;
    for(int i = 0; i < n - 1; i++){
        int a, b;
        cin >> a >> b;
        g[a].push_back(b);
        g[b].push_back(a);
    }
    for(int i = 0; i < n; i++){
        a[i + 1] = (str[i] == '(' ? 1 : -1);
    }
    calc(1);
    cout << ans << '\n';

}