#include <iostream>
#include <string>
#include <queue>
#include <stack>
#include <algorithm>
#include <math.h>
#include <vector>
#include <cstring>
#include <ctime>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <iomanip>
#include <ctime>
#define fr first
#define sc second
#define MP make_pair
#define PB push_back
#define fastio ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define lli long long int
#define y1 arayikhalatyan
using namespace std;
lli gcd(lli a, lli b) {
if (b == 0)
return a;
return gcd(b, a % b);
}
lli cg(lli n) {
return n ^ (n >> 1);
}
lli SUM(lli a)
{
return (a * (a + 1) / 2);
}
bool CAN(int x, int y, int n, int m)
{
if (x >= 0 && y >= 0 && x < n && y < m)
{
return true;
}
return false;
}
double her(double x1, double y1, double x2, double y2)
{
return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
string strsum(string a, string b)
{
int p = 0;
string c;
reverse(a.begin(), a.end());
reverse(b.begin(), b.end());
if (b.length() < a.length())
{
for (int i = b.length(); i < a.length(); i++)
{
b += "0";
}
}
else
{
for (int i = a.length(); i < b.length(); i++)
{
a += "0";
}
}
a += "0", b += "0";
for (int i = 0; i < a.length(); i++)
{
c += (a[i] - '0' + b[i] - '0' + p) % 10 + '0';
p = (a[i] + b[i] - '0' - '0' + p) / 10;
}
if (c[c.length() - 1] == '0') c.erase(c.length() - 1, 1);
reverse(c.begin(), c.end());
return c;
}
string strmin(string a, string b)
{
if (a.length() > b.length()) return b;
if (b.length() > a.length()) return a;
for (int i = 0; i < a.length(); i++)
{
if (a[i] > b[i]) return b;
if (b[i] > a[i]) return a;
}
return a;
}
char vow[] = { 'a', 'e', 'i', 'o', 'u' };
int dx[] = { 1, -1, 0, 0 };
int dy[] = { 0, 0, 1, -1 };
const int N = 1e6 + 30;
const lli mod = 1000000007;
int mn(int a, int b)
{
if (a < b) return a;
return b;
}
int n, sm;
string s;
vector <int> g[N];
bool col[N];
int qan[N];
queue <int> h;
lli nerq[2 * N], ver[2 * N];
lli pat;
vector <int> ss;
void dfsqan(int v, int par)
{
qan[v] = 1;
for (auto p : g[v])
{
if (p != par && !col[p])
{
dfsqan(p, v);
qan[v] += qan[p];
}
}
}
void dfshashvv(int v, int par, int min, int val)
{
if (s[v - 1] == '(')
{
val++;
min = mn(1, min + 1);
if (min >= 0) ver[val + N]++, ss.PB(val + N);
}
else min = mn(-1, min - 1), val--;
for (auto p : g[v])
{
if (p != par && !col[p])
{
dfshashvv(p, v, min, val);
}
}
}
void dfshashvn(int v, int par, int min, int val)
{
if (s[v - 1] == '(') val++;
else
{
val--;
if (val <= min) nerq[N + val]++, ss.PB(N + val);
min = mn(val, min);
}
//cout << v << "_" << val << endl;
for (auto p : g[v])
{
if (p != par && !col[p])
{
dfshashvn(p, v, min, val);
}
}
}
void dfspatn(int v, int par, int min, int val)
{
if (s[v - 1] == '(') val++;
else
{
val--;
if (val <= min) pat += ver[N - val];
min = mn(val, min);
}
for (auto p : g[v])
{
if (p != par && !col[p])
{
dfspatn(p, v, min, val);
}
}
}
void dfspatv(int v, int par, int min, int val)
{
if (s[v - 1] == '(')
{
val++;
min = mn(1, min + 1);
if (min >= 0) pat += nerq[N - val];
}
else min = mn(-1, min - 1), val--;
for (auto p : g[v])
{
if (p != par && !col[p])
{
dfspatv(p, v, min, val);
}
}
}
void dfsc(int v, int par)
{
bool flag = true;
for (auto p : g[v])
{
if (p != par && !col[p])
{
if (qan[p] > sm)
{
dfsc(p, v);
flag = false;
}
}
}
if (flag)
{
//cout << v << " ";
col[v] = true;
int val, min;
if (s[v - 1] == '(') val = 1, min = 0;
else val = -1, min = -1, nerq[N - 1]++, ss.PB(N - 1);
for (auto p : g[v])
{
if (!col[p])
{
h.push(p);
dfspatn(p, v, min, val);
dfspatv(p, v, 0, 0);
dfshashvn(p, v, min, val);
dfshashvv(p, v, 0, 0);
}
}
pat += nerq[N];
if (val == 1) pat += ver[N - 1];
for (auto p : ss) nerq[p] = 0, ver[p] = 0;
ss.clear();
//cout << pat << endl;
}
}
int main()
{
fastio;
cin >> n >> s;
for (int i = 0; i < n - 1; i++)
{
int a, b;
cin >> a >> b;
g[a].PB(b);
g[b].PB(a);
}
h.push(1);
while (!h.empty())
{
int k = h.front();
h.pop();
//cout << "k-" << k << endl;
dfsqan(k, -1);
sm = qan[k] / 2;
dfsc(k, -1);
}
cout << pat;
return 0;
}
