#include <bits/stdc++.h>
using namespace std;
typedef long long lint;
typedef pair<int, int> pi;
int n;
char a[300005];
int sz[300005], msz[300005], vis[300005];
vector<int> gph[300005];
vector<int> dfn;
void dfs(int x, int p){
dfn.push_back(x);
sz[x] = 1;
msz[x] = 0;
for(auto &i : gph[x]){
if(vis[i] || i == p) continue;
dfs(i, x);
msz[x] = max(msz[x], sz[i]);
sz[x] += sz[i];
}
}
int get_center(int x){
dfn.clear();
dfs(x, -1);
int cur = 1e9;
int ret = -1;
for(auto &i : dfn){
int w = max(msz[i], (int)dfn.size() - sz[i]);
if(cur > w){
cur = w;
ret = i;
}
}
return ret;
}
void dfs2(int x, int p, vector<int> &v, int dep, int mdep){
if(a[x] == '(') dep++;
else dep--;
mdep = max(mdep, dep);
if(mdep == dep) v.push_back(dep);
for(auto &i : gph[x]){
if(!vis[i] && i != p) dfs2(i, x, v, dep, mdep);
}
}
void dfs3(int x, int p, vector<int> &v, int dep, int mdep){
if(a[x] == '(') dep--;
else dep++;
mdep = max(mdep, dep);
if(mdep == dep) v.push_back(dep);
for(auto &i : gph[x]){
if(!vis[i] && i != p) dfs3(i, x, v, dep, mdep);
}
}
int cnt[300005];
lint getp(int x, vector<int> &l, vector<int> &r){
lint ans = 0;
for(auto &i : r) cnt[i]++;
for(auto &i : l) ans += cnt[i];
for(auto &i : r) cnt[i]--;
return ans;
}
lint solve(int x){
vector<int> l, r;
lint sum = 0;
int flg = (a[x] == '(' ? -1 : 1);
for(auto &i : gph[x]){
if(vis[i]) continue;
vector<int> tl, tr;
dfs2(i, x, tl, 0, 0);
dfs3(i, x, tr, flg, max(flg, 0));
for(auto &i : tl){
l.push_back(i);
if(flg == i) sum++;
}
for(auto &i : tr){
r.push_back(i);
if(i == 0) sum++;
}
sum -= getp(flg, tl, tr);
}
sum += getp(flg, l, r);
return sum;
}
int main(){
scanf("%d %s",&n,a+1);
for(int i=1; i<n; i++){
int s, e;
scanf("%d %d",&s,&e);
gph[s].push_back(e);
gph[e].push_back(s);
}
queue<int> que;
que.push(1);
lint ans = 0;
while(!que.empty()){
int x = que.front();
que.pop();
x = get_center(x);
ans += solve(x);
vis[x] = 1;
for(auto &i : gph[x]){
if(!vis[i]) que.push(i);
}
}
cout << ans;
}
