// I don't know ..
#include<bits/stdc++.h>
using namespace std;
const int N = 300005;
int n, M[N], SZ[N], C[N];
char S[N];
long long tot;
vector < int > Adj[N];
pair < int , int > dp[N], pd[N];
void DFSSZ(int v, int p = 0)
{
SZ[v] = 1;
for (int u : Adj[v])
if (u != p && !M[u])
DFSSZ(u, v), SZ[v] += SZ[u];
}
int Centroid(int v, int p, int _n)
{
for (int u : Adj[v])
if (!M[u] && u != p && SZ[u] * 2 > _n)
return Centroid(u, v, _n);
return v;
}
void DFSC(int v, int p)
{
dp[v] = {dp[p].first + S[v], min(dp[p].second + S[v], 0)};
pd[v] = {pd[p].first - S[v], min(pd[p].second - S[v], 0)};
for (int u : Adj[v])
if (u != p && !M[u])
DFSC(u, v);
}
void DFSADD(int v, int p, int tp)
{
if (dp[v].second >= 0)
C[dp[v].first] += tp;
for (int u : Adj[v])
if (!M[u] && u != p)
DFSADD(u, v, tp);
}
void DFSGT(int v, int p)
{
if (pd[v].second >= 0)
tot += C[pd[v].first];
for (int u : Adj[v])
if (!M[u] && u != p)
DFSGT(u, v);
}
inline void Solve(int v)
{
dp[v] = {S[v], min((int)S[v], 0)};
pd[v] = {0, 0};
for (int u : Adj[v])
if (!M[u])
DFSC(u, v);
for (int u : Adj[v])
if (!M[u])
DFSADD(u, v, 1);
tot += C[0];
if (dp[v].second >= 0)
C[dp[v].first] ++;
for (int u : Adj[v])
if (!M[u])
DFSADD(u, v, -1), DFSGT(u, v), DFSADD(u, v, 1);
for (int u : Adj[v])
if (!M[u])
DFSADD(u, v, -1);
if (dp[v].second >= 0)
C[dp[v].first] --;
}
inline void Decompose()
{
queue < int > qu;
qu.push(1);
while (qu.size())
{
int v = qu.front();
DFSSZ(v);
v = Centroid(v, 0, SZ[v]);
qu.pop(); M[v] = 1;
Solve(v);
for (int u : Adj[v])
if (!M[u]) qu.push(u);
}
}
int main()
{
scanf("%d%s", &n, S + 1);
for (int i = 1; i <= n; i ++)
S[i] = (S[i] == '(' ? 1 : -1);
for (int i = 1; i < n; i ++)
{
int v, u;
scanf("%d%d", &v, &u);
Adj[v].push_back(u);
Adj[u].push_back(v);
}
Decompose();
return !printf("%lld\n", tot);
}
