#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define N 200000
#define INF 0x3f3f3f3f
int dd[N], kk[N];
int *ej[N], eo[N], eo_[N];
void append(int i, int j) {
int o = eo[i]++;
if (o >= 2 && (o & o - 1) == 0)
ej[i] = (int *) realloc(ej[i], o * 2 * sizeof *ej[i]);
ej[i][o] = j;
}
int d_; long long k_;
void dfs(int i) {
int o, d, k;
if (eo_[i] != 1)
return;
eo_[i] = 0;
d = dd[i] + 1, k = kk[i];
for (o = eo[i]; o--; ) {
int j = ej[i][o];
if (eo_[j] > 0) {
if (d_ < dd[j] + d)
d_ = dd[j] + d, k_ = 0;
if (d_ == dd[j] + d)
k_ += (long long) kk[j] * k;
if (dd[j] < d)
dd[j] = d, kk[j] = 0;
if (dd[j] == d)
kk[j] += k;
eo_[j]--, dfs(j);
return;
}
}
}
int main() {
static int ii[N], dp[N], kp[N], dq[N], kq[N];
int n, m, h, i, j, o, d;
long long k;
scanf("%d", &n);
for (i = 0; i < n; i++)
ej[i] = (int *) malloc(2 * sizeof *ej[i]);
for (h = 0; h < n; h++) {
scanf("%d%d", &i, &j), i--, j--;
append(i, j), append(j, i);
}
memcpy(eo_, eo, n * sizeof *eo);
for (i = 0; i < n; i++)
dd[i] = 0, kk[i] = 1;
for (i = 0; i < n; i++)
dfs(i);
m = 0;
for (i = 0; i < n; i++)
if (eo_[i] > 0) {
while (eo_[i] > 0) {
eo_[i] = 0, ii[m++] = i;
for (o = eo[i]; o--; ) {
j = ej[i][o];
if (eo_[j] > 0) {
i = j;
break;
}
}
}
break;
}
if (m > 1) {
d = -INF, k = 0;
for (h = 0; h < m; h++) {
i = ii[h];
if (h == m / 2)
d = -INF, k = 0;
if (d < dd[i] - h)
d = dd[i] - h, k = 0;
if (d == dd[i] - h)
k += kk[i];
dp[h] = d, kp[h] = k;
}
d = -INF, k = 0;
for (h = m - 1; h >= 0; h--) {
i = ii[h];
if (h == m / 2 - 1)
d = -INF, k = 0;
if (d < dd[i] - h)
d = dd[i] - h, k = 0;
if (d == dd[i] - h)
k += kk[i];
dq[h] = d, kq[h] = k;
}
for (h = 0; h < m; h++) {
i = ii[h];
if (h < m / 2) {
if (h > 0) {
d = dp[h - 1] + dd[i] + h, k = (long long) kp[h - 1] * kk[i];
if (d_ < d)
d_ = d, k_ = 0;
if (d_ == d)
k_ += k;
}
d = dq[h + (m + 1) / 2] + dd[i] + m + h, k = (long long) kq[h + (m + 1) / 2] * kk[i];
if (d_ < d)
d_ = d, k_ = 0;
if (d_ == d)
k_ += k;
} else {
if (h > m / 2) {
d = dp[h - 1] + dd[i] + h, k = (long long) kp[h - 1] * kk[i];
if (d_ < d)
d_ = d, k_ = 0;
if (d_ == d)
k_ += k;
}
if (h + 1 < m || m % 2 == 0) {
d = dq[h - m / 2] + dd[i] + h, k = (long long) kq[h - m / 2] * kk[i];
if (d_ < d)
d_ = d, k_ = 0;
if (d_ == d)
k_ += k;
}
}
}
}
printf("%lld\n", k_);
return 0;
}
