#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
#define mp make_pair
#define pb push_back
#define F first
#define S second
#define debug(x) std::cout << #x << ": " << x << "\n"
#define all(v) v.begin(), v.end()
#define li(i,a,b) for (int (i) = (a); (i) < (b); (i)++)
#define endl '\n'
#define mem(name,val) memset(name,val,sizeof(name))
#define min(a,b) (a<=b ? a : b)
#define max(a,b) (a>=b ? a : b)
//using u64 = uint64_t;
//using u128 = __uint128_t;
const int nmax = 3e5+10;
int l[nmax],sz[nmax],r[nmax];
vector<int> adj[nmax];
int dfs_sz(int u, int par=-1){
sz[u]=1;
for(int v:adj[u]){
if(v==par || r[v])continue;
sz[u]+=dfs_sz(v,u);
}
return sz[u];
}
int get_cent(int u, int ts, int par=-1){
for(int v : adj[u]){
if(par==v || r[v])continue;
if(sz[v]*2>ts)return get_cent(v,ts,u);
}
return u;
}
int rcnt[2*nmax],lcnt[2*nmax];
int res=0;
void slv_cent(int u, int par, bool fill, int v, int minv, int maxv, int root){
v+=l[u];
minv=min(minv,v);
maxv=max(maxv,v);
// valid left
if(v >= maxv){
if(fill){
res+=rcnt[-(v+l[root])+nmax];
}
else{
lcnt[v+nmax]++;
}
}
// valid right
if(v <= minv){
if(fill){
res+=lcnt[-(v+l[root])+nmax];
}
else{
rcnt[v+nmax]++;
}
}
for(int to : adj[u]){
if(to==par||r[to])continue;
slv_cent(to,u,fill,v,minv,maxv,root);
}
}
void del(int u, int par, int v){
v+=l[u];
lcnt[v+nmax]=rcnt[v+nmax]=0;
for(int to : adj[u]){
if(to==par||r[to])continue;
del(to,u,v);
}
}
void solve(int u){
u = get_cent(u,dfs_sz(u));
r[u]=1;
lcnt[nmax]++;
rcnt[nmax]++;
for(int v : adj[u]){
if(r[v])continue;
slv_cent(v,u,true,0,0,0,u);
slv_cent(v,u,false,0,0,0,u);
}
// clear l/r cnt
lcnt[nmax]=rcnt[nmax]=0;
for(int v:adj[u]){
if(r[v])continue;
del(v,u,0);
}
for(int v:adj[u]){
if(r[v])continue;
solve(v);
}
}
int main()
{
ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
char in;
int n;
cin>>n;
li(i,1,n+1){
cin>>in;
l[i]=(in=='('?1:-1);
}
int a,b;
li(i,0,n-1){
cin>>a>>b;
adj[a].pb(b);
adj[b].pb(a);
}
mem(r,0);
mem(rcnt,0);
mem(lcnt,0);
solve(1);
cout<<res;
return 0;
}
