/** MIT License Copyright (c) 2018 Vasilyev Daniil **/
#include <bits/stdc++.h>
//#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
template<typename T> using v = vector<T>;
//template<typename T, typename U> using hmap = __gnu_pbds::gp_hash_table<T, U>;
typedef long long longlong;
#define int longlong
typedef long double ld;
typedef string str;
typedef vector<int> vint;
#define rep(a, l, r) for(int a = (l); a < (r); a++)
#define pb push_back
#define fs first
#define sc second
#define sz(a) ((int) a.size())
const long long inf = 4611686018427387903; //2^62 - 1
#if 0 //FileIO
const string fileName = "";
ifstream fin ((fileName == "" ? "input.txt" : fileName + ".in" ));
ofstream fout((fileName == "" ? "output.txt" : fileName + ".out"));
#define get fin>>
#define put fout<<
#else
#define get cin>>
#define put cout<<
#endif
#define eol put endl
void read() {} template<typename Arg,typename... Args> void read (Arg& arg,Args&... args){get (arg) ;read(args...) ;}
void print(){} template<typename Arg,typename... Args> void print(Arg arg,Args... args){put (arg)<<" ";print(args...);}
int getInt(){int a; get a; return a;}
int popcount(int a) { return __builtin_popcount(a); }
//code goes here
const int N = 3e5 + 1;
vector<int> t[N]; //init me
int siz[N];
bitset<N> added;
int vals[N];
int calcSize(int cur, int p) {
siz[cur] = 1;
for (auto i : t[cur])
if (!added.test(i) && i != p)
siz[cur] += calcSize(i, cur);
return siz[cur];
}
map<int, int> dist[N];
int p;
map<int, int> allDist;
void addDistances(int cur, int l, int r, int par = -1) {
if (l == 0) {
allDist[r]++;
dist[p][r]++;
}
for (int i : t[cur])
if (!added.test(i) && i != par) {
if (vals[i] == 1)
addDistances(i, l + 1, r, cur);
else
addDistances(i, max(0ll, l - 1), r + (l == 0), cur);
}
}
int ans = 0;
void checkDistances(int cur, int l, int r, int par = -1) {
if (r == 0)
ans += allDist[l] - dist[p][l];
for (int i : t[cur])
if (!added.test(i) && i != par) {
if (vals[i] == 1)
checkDistances(i, l + (r == 0), max(0ll, r - 1), cur);
else
checkDistances(i, l, r + 1, cur);
}
}
void solve(int cur) {
allDist.clear();
p = 0;
int l = vals[cur] == 1, r = vals[cur] == -1;
for (auto i : t[cur])
if (!added.test(i)) {
dist[p].clear();
if (vals[i] == 1)
addDistances(i, l + 1, r, cur);
else
addDistances(i, max(0ll, l - 1), r + (l == 0), cur);
p++;
}
if (vals[cur] == -1)
allDist[1]++;
else
ans += allDist[0];
p = 0;
for (auto i : t[cur])
if (!added.test(i)) {
checkDistances(i, vals[i] == 1, vals[i] == -1);
p++;
}
}
void find_centroid(int cur) {
int lim = calcSize(cur, -1) / 2;
int pr = -1;
for (bool again = 1; again;) {
again = 0;
for (auto i : t[cur])
if (!added.test(i) && i != pr && siz[i] > lim) {
pr = cur;
cur = i;
again = 1;
break;
}
}
added.set(cur);
solve(cur);
for (auto i : t[cur])
if (!added.test(i))
find_centroid(i);
}
void run() {
int n;
get n;
str s;
get s;
rep(i, 1, n + 1)
if (s[i - 1] == '(')
vals[i] = 1;
else
vals[i] = -1;
rep(i, 1, n) {
int v, u;
read(v, u);
t[v].pb(u);
t[u].pb(v);
}
find_centroid(1);
put ans;
}
signed main() {srand(time(0)); ios::sync_with_stdio(0); cin.tie(0); put fixed << setprecision(15); run(); return 0;}
