#include <bits/stdc++.h>

using namespace std;

#define ss second
#define ff first
#define p_b push_back
#define endl "\n"

typedef long long ll;
typedef long double ld;

const ll INF = 2e18;
const ll INFINT = 2e9;
const int N = 1000006;
const int NN = 1006;

ll ans = 0;
int n;
int CR = 10;
int sz[N];
bool wasCentroid[N];
int startbal, last[2][N];
vector < int > g[N];
string s;
vector < int > kek[2];

void Calc_Size (int v, int p = -1) {
    sz[v] = 1;
    for (int to : g[v]) {
        if (to == p || wasCentroid[to]) continue;
        Calc_Size(to, v);
        sz[v] += sz[to];
    }
}

int Find_Centroid (int v, int p = -1, int SZ = -1) {
    if (p == -1) SZ = sz[v];
    for (int to : g[v]) {
        if (to == p || wasCentroid[to]) continue;
        if (sz[to] < SZ / 2) continue;
        return Find_Centroid(to, v, SZ);
    }
    return v;
}

void dfs_fnd_pre (int v, int p, int bal) {
    //cerr << "FND PRE " << bal << endl;
    if (s[v] == '(') bal++;
    else bal--;
    if (bal >= 0 && bal + startbal >= 0 && s[v] == '(') {
       // cout << "PRE " << v << ' ' << bal << ' ' << kek[1][bal + startbal] << endl;
        if (last[1][bal + startbal] != CR) {
            last[1][bal + startbal] = CR;
            kek[1][bal + startbal] = 0;
        }
      //  cout << "PREF " << v + 1 << ' ' << bal << ' ' << kek[1][bal + startbal] << endl;
        ans += kek[1][bal + startbal];
    }
    for (int to : g[v]) {
        if (to == p || wasCentroid[to]) continue;
        dfs_fnd_pre(to, v, bal);
    }
}

void dfs_fnd_suff (int v, int p, int bal) {
    //cerr << "FND SUFF " << bal << endl;
    if (s[v] == '(') bal++;
    else bal--;
    if (bal <= 0 && bal + startbal <= 0 && s[v] == ')') {
        if (last[0][-(bal + startbal)] != CR) {
            last[0][-(bal + startbal)] = CR;
            kek[0][-(bal + startbal)] = 0;
        }
       // cout << "SUFF " << v << ' ' << bal << ' ' << kek[0][bal + startbal] << endl;
      //  cout << "SUFF " << v + 1 << ' ' << bal << ' ' << kek[0][-(bal + startbal)] << endl;
        ans += kek[0][-(bal + startbal)];
    }
    for (int to : g[v]) {
        if (to == p || wasCentroid[to]) continue;
        dfs_fnd_suff(to, v, bal);
    }
}

void dfs_pls_pre (int v, int p, int bal) {
    //cerr << "PLS PRE " << bal << endl;
    if (s[v] == '(') bal++;
    else bal--;
    if (bal + startbal >= 0 && s[v] == '(') {
        if (last[0][bal] != CR) {
            last[0][bal] = CR;
            kek[0][bal] = 0;
        }
        kek[0][bal]++;
    }
    for (int to : g[v]) {
        if (to == p || wasCentroid[to]) continue;
        dfs_pls_pre(to, v, bal);
    }
}

void dfs_pls_suff (int v, int p, int bal) {
    //cerr << "PLS SUFF " << bal << endl;
    if (s[v] == '(') bal++;
    else bal--;
    if (bal + startbal <= 0 && s[v] == ')') {
        if (last[1][-bal] != CR) {
            last[1][-bal] = CR;
            kek[1][-bal] = 0;
        }
        kek[1][-bal]++;
    }
    for (int to : g[v]) {
        if (to == p || wasCentroid[to]) continue;
        dfs_pls_suff(to, v, bal);
    }
}

void go (int v) {
    Calc_Size(v);
    v = Find_Centroid(v);
    CR++;
    //cout << "CENTR  " << 1 + v << endl;
    //cerr << v << endl;//

    //cout << "CENTROID " << v << endl;


    //kek[0].assign (kek[0].size(), 0);
    //kek[1].assign (kek[1].size(), 0);
    kek[0][0] = kek[1][0] = 1;
    last[0][0] = last[1][0] = CR;

    if (s[v] == '(') startbal = 1;
    else startbal = -1;

    for (int to : g[v]) {
        //cerr << to << endl;
        if (wasCentroid[to]) continue;

        dfs_fnd_pre(to, v, 0);
        dfs_fnd_suff(to, v, 0);

        dfs_pls_pre(to, v, 0);
        dfs_pls_suff(to, v, 0);
        //cout << to + 1 << endl;
       // cout << ans << endl;
        //for (int i = 0; i < n; i++) cout << kek[0][i] << ' ' << kek[1][i] << endl;
       // cout << endl;
    }
//exit(0);
    wasCentroid[v] = 1;
    for (int i = 0; i < g[v].size(); i++) {
        if (wasCentroid[g[v][i]]) continue;
        go(g[v][i]);
    }
}

int main () {
    ios_base::sync_with_stdio(0);
#ifdef LOCAL
    freopen ("input.txt", "r", stdin);
    freopen ("output.txt", "w", stdout);
#else
    //freopen ("input.txt", "r", stdin);freopen ("output.txt", "w", stdout);
    //freopen ("dynamic.in", "r", stdin);freopen ("dynamic.out", "w", stdout);
#endif // LOCAL
    cin >> n;
    cin >> s;
    for (int i = 0; i < n - 1; i++) {
        int x, y;
        cin >> x >> y;
        x--, y--;
        g[x].p_b(y);
        g[y].p_b(x);
    }
    kek[0].resize(n + 10);
    kek[1].resize(n + 10);
    go(0);
    cout << ans << endl;
}