23. Let $p$ be a prime number, and $n$ be a positive integer.
(i) Find the formula for $e$ in $p^{e} \|(2 n)!$, where
$$(2 n)!!=(2 n)(2 n-2) \cdots 2$$
(ii) Find the formula for $f$ in $p^{f} \|(2 n+1)!!$, where
$$(2 n-1)!!=(2 n-1)(2 n-3) \cdots 1$$
23. (i) When $p=2$, $e=n+\sum_{j}\left[n / 2^{j}\right] ;$ when $p>2$, $e=\sum_{j}\left[n / p^{j}\right]$.
(ii) When $p=2$, $f=0 ;$ when $p>2$, $f=\sum_{j}\left(\left[2 n / p^{j}\right]-\left[n / p^{j}\right]\right)$.