#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define ll long long
#define all(x) (x).begin(), (x).end()
const int mxn = 3e5 + 10;
int n;
string s;
int sz[mxn];
vector<int> g[mxn];
bool processed[mxn];
int getSize(int cur = 1, int par = -1) {
sz[cur] = 1;
for (auto x : g[cur]) {
if (x != par && !processed[x]) sz[cur] += getSize(x, cur);
}
return sz[cur];
}
int getCentroid(int cur, int des, int par = -1) {
for (auto x : g[cur]) {
if (x != par && !processed[x] && sz[x] >= des) return getCentroid(x, des, cur);
}
return cur;
}
ll ans = 0, cntL[mxn], cntR[mxn];
int mx = 0;
// L - side
void get1(int cur, int open, int close, int par = -1) {
// cout << "?1 " << cur << " " << open << " " << close << " " << par << endl;
if (close == 0) ans += cntR[open];
for (auto x : g[cur]) {
if (x != par && !processed[x]) {
if (s[x] == '(') {
if (close) get1(x, open, close - 1, cur);
else get1(x, open + 1, close, cur);
}
if (s[x] == ')') get1(x, open, close + 1, cur);
}
}
}
// R - side
void get2(int cur, int open, int close, int par = -1) {
// cout << "?2 " << cur << " " << open << " " << close << " " << par << endl;
if (open == 0) ans += cntL[close];
for (auto x : g[cur]) {
if (x != par && !processed[x]) {
if (s[x] == ')') {
if (open) get2(x, open - 1, close, cur);
else get2(x, open, close + 1, cur);
}
if (s[x] == '(') get2(x, open + 1, close, cur);
}
}
}
// L - side
void update1(int cur, int open, int close, int par = -1) {
// cout << "!1 " << cur << " " << open << " " << close << " " << par << endl;
if (close == 0) {
cntL[open]++;
mx = max(mx, open);
}
for (auto x : g[cur]) {
if (x != par && !processed[x]) {
if (s[x] == '(') {
if (close) update1(x, open, close - 1, cur);
else update1(x, open + 1, close, cur);
}
if (s[x] == ')') update1(x, open, close + 1, cur);
}
}
}
// R - side
void update2(int cur, int open, int close, int par = -1) {
// cout << "!2 " << cur << " " << open << " " << close << " " << par << endl;
if (open == 0) {
cntR[close]++;
mx = max(mx, close);
}
for (auto x : g[cur]) {
if (x != par && !processed[x]) {
if (s[x] == '(') update2(x, open + 1, close, cur);
if (s[x] == ')') {
if (open) update2(x, open - 1, close, cur);
else update2(x, open, close + 1, cur);
}
}
}
}
void decompose(int cur = 1, int par = -1) {
int centroid = getCentroid(cur, getSize(cur) / 2);
processed[centroid] = 1;
cntL[0] = cntR[0] = 1;
int open = s[centroid] == '(', close = s[centroid] == ')';
for (auto x : g[centroid]) {
if (x != par && !processed[x]) {
if (s[x] == '(') {
if (close) get1(x, open, close - 1, centroid);
else get1(x, open + 1, close, centroid);
get2(x, open + 1, close, centroid);
}
if (s[x] == ')') {
get1(x, open, close + 1, centroid);
if (open) get2(x, open - 1, close, centroid);
else get2(x, open, close + 1, centroid);
}
if (s[x] == '(') {
update1(x, 1, 0, centroid);
update2(x, 1, 0, centroid);
}
if (s[x] == ')') {
update1(x, 0, 1, centroid);
update2(x, 0, 1, centroid);
}
}
}
// cout << centroid << " " << ans << endl;
for (auto x : g[centroid]) {
if (x != par && !processed[x]) {
for (int i = 0; i <= mx; i++) cntL[i] = cntR[i] = 0;
mx = 0;
decompose(x, centroid);
}
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> n;
cin >> s;
s = "." + s;
for (int i = 0; i < n - 1; i++) {
int f, t;
cin >> f >> t;
g[f].push_back(t);
g[t].push_back(f);
}
decompose();
cout << ans;
}
