#include <bits/stdc++.h>
#define pb push_back
#define X first
#define Y second
using namespace std;
typedef long long int ll;
typedef vector<int> vi;
typedef pair<int, int> pii;
struct zagrade {
int maxpref=0, minpref=0, val=0;
};
const int MAXN = 3e5+7;
string str;
int bio[MAXN], cent[MAXN], sz[MAXN];
vector<vi> komp; map<int, int> cnt;
map<char, int> mapa = {{'(', 1}, {')', -1}};
zagrade zag[MAXN];
vi sus[MAXN];
int br = 1, centroid, n;
ll sol = 0;
void dfs2(int x) {
bio[x] = br; komp.back().pb(x);
if (str[x-1] == '(') ++zag[x].val;
else --zag[x].val;
zag[x].minpref = min(zag[x].minpref, zag[x].val);
zag[x].maxpref = max(zag[x].maxpref, zag[x].val);
if (zag[x].val-zag[x].minpref <= 0) {
++cnt[-(zag[x].minpref)];
}
for (auto y: sus[x]) {
if (bio[y] == br or cent[y] or y == x) continue;
zag[y] = zag[x]; dfs2(y);
}
}
void dfs(int x) {
bio[x] = br;
if (br > 1) sz[x] = 1;
for (auto y: sus[x]) {
if (cent[y] or bio[y] == br) continue;
bio[y] = br; dfs(y);
if (br > 1) sz[x] += sz[y];
}
}
void nadi(int x, int cvor) {
if (sz[x]-1 >= sz[cvor]/2) centroid = x;
bio[x] = br;
for (auto y: sus[x]) {
if (cent[y] or bio[y] == br) continue;
nadi(y, cvor);
}
}
void centroidna(int cvor) {
cnt = {}, komp = {};
++br; dfs(cvor); ++br; nadi(cvor, cvor);
cent[centroid] = 1;
for (auto x: sus[centroid]) {
if (cent[x] == 0) {
komp.push_back({}); ++br; dfs2(x);
}
}
++cnt[0]; //komp = {{7, 5, 4}, {1, 3, 6}};
for (auto v: komp) {
for (auto x: v) {
if (zag[x].val-zag[x].minpref <= 0) {
--cnt[-(zag[x].minpref)];
}
}
for (auto x: v) {
int val2 = zag[x].val+mapa[str[centroid-1]];
int maxpf = max(0, zag[x].maxpref+mapa[str[centroid-1]]);
if (val2-maxpf >= 0) sol += cnt[maxpf];
}
for (auto x: v) {
if (zag[x].val-zag[x].minpref <= 0) {
++cnt[-(zag[x].minpref)];
}
}
}
for (auto v: komp) {
for (auto x: v) zag[x] = {0, 0, 0};
}
if (str[centroid-1] == '(') sol += cnt[1];
for (auto x: sus[centroid]) {
if (cent[x] == 0) centroidna(x);
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
cin >> n >> str;
for (int i=0; i<n-1; ++i) {
int a, b; cin >> a >> b;
sus[a].pb(b); sus[b].pb(a);
}
dfs(1); centroidna(1);
cout << sol;
return 0;
}
