#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
//#include <ext/pb_ds/tree_policy.hpp>
//#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
//using namespace __gnu_pbds;
#define FOR(i,start,end) for(int i=start;i<(int)(end);i++)
#define FORE(i,start,end) for(int i=start;i<=(int)end;i++)
#define RFOR(i,start,end) for(int i = start; i>end; i--)
#define RFORE(i,start,end) for(int i = start; i>=end; i--)
#define all(a) a.begin(), a.end()
#define mt make_tuple
#define mp make_pair
#define v vector
#define sf scanf
#define pf printf
#define dvar(x) cout << #x << " := " << x << "\n"
#define darr(x,n) FOR(i,0,n) cout << #x << "[" << i << "]" << " := " << x[i] << "\n"
typedef long long ll;
typedef long double ld;
typedef pair<int, int > pii;
typedef pair<ll, ll> pll;
//template <class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T> void minn(T &a, T b) { a = min(a, b); }
template<class T> void maxx(T &a, T b) { a = max(a, b); }
void io() {
#ifdef LOCAL_PROJECT
freopen("input.in", "r", stdin); freopen("output.out", "w", stdout);
#else
/* online submission */
#endif
ios_base::sync_with_stdio(false); cin.tie(NULL);
}
const ll MOD = 1000000007LL;
const ll PRIME = 105943LL;
const ll INF = 1e18;
/****************************************************************/
const int MAXN = 300099;
int N, A[MAXN];
set<int> adj[MAXN];
int subtreeSize[MAXN];
ll ans = 0;
int computeSSize(int cur, int par) {
subtreeSize[cur] = 1;
for (auto neigh : adj[cur]) if (neigh != par)
subtreeSize[cur] += computeSSize(neigh, cur);
return subtreeSize[cur];
}
int getCentroid(int cur, int par) {
computeSSize(cur, par);
int maxsize = subtreeSize[cur] / 2; // all subtrees must be <= maxsize
while (true) {
int next = -1; // is there a child of cur with size > maxsize?
for (auto neigh : adj[cur]) { // check all childs of cur
if (neigh != par && subtreeSize[neigh] > maxsize) {
next = neigh;
break;
}
}
if (next == -1) { // cur is a centroid
return cur;
}
par = cur;
cur = next;
}
return -10000; // ERROR
}
struct dat {
int x, u, d;
dat(int a, int b, int c) : x(a), u(b), d(c) {}
};
void dfs(int i, int p, v<dat> &tab, int pidx) {
if (pidx == -1) {
tab.push_back(dat(A[i], A[i], A[i]));
}
else {
dat cur(0, 0, 0);
cur.x = A[i] + tab[pidx].x;
cur.u = min(A[i], A[i] + tab[pidx].u);
cur.d = min(tab[pidx].d, cur.x);
tab.push_back(cur);
}
int iidx = tab.size() - 1;
for (auto c : adj[i]) if (c != p) {
dfs(c, i, tab, iidx);
}
}
void dfsSolve(int root) {
root = getCentroid(root, -1);
int R = A[root];
// cout << root << " root \n";
v<v<dat>> table;
map<int, int> cnt;
for (auto c : adj[root]) {
table.push_back(v<dat>());
dfs(c, root, table.back(), -1);
for (auto t : table.back()) {
if (t.x + R == 0 && t.u >= 0)
ans++;
if (t.x + R == 0 && t.d + R >= 0 && R >= 0)
ans++;
if (t.d >= t.x)
cnt[t.x]++;
}
// cout << c << ":\n";
// for (auto t : table.back())
// cout << t.x << " x " << t.u << " u " << t.d << " d \n";
}
for (auto &sub : table) {
for (auto t : sub) if (t.d >= t.x) cnt[t.x]--;
for (auto t : sub) {
if (t.u >= 0 && t.x + R >= 0) {
auto it = cnt.find(-(t.x + R));
if (it != cnt.end())
ans += it->second;
}
}
for (auto t : sub) if (t.d >= t.x) cnt[t.x]++;
}
for (int subt : adj[root]) {
adj[subt].erase(root);
dfsSolve(subt);
}
}
int main() {
io();
cin >> N;
string s;
cin >> s;
FOR(i, 0, N) A[i + 1] = s[i] == '(' ? 1 : -1;
FOR(i, 0, N - 1) {
int a, b;
cin >> a >> b;
adj[a].insert(b), adj[b].insert(a);
}
dfsSolve(1);
cout << ans << "\n";
return 0;
}
