Mafia

$n$ mobsters face off in a tense standoff. Each mobster has drawn a pistol and permanently aims it at exactly one of the $n$ mobsters (possibly at himself). If the shooting begins, it proceeds under this code of honour:

• The mobsters fire one at a time, in some order; at any moment at most one shot is fired.
• No shooter ever misses. The target dies instantly and can no longer fire.
• Every mobster fires exactly once, unless he is killed before his turn to shoot arrives.
• A mobster never changes his chosen target. If that target is already dead when he fires, the shot merely hits a corpse and causes no new casualty.

The order in which the mobsters shoot is not fixed, and different orders can lead to a different number of deaths. Knowing only who aims at whom, determine the minimum and the maximum possible number of casualties over all shooting orders.

The first line contains one integer $n$ ($1 \le n \le 1{,}000{,}000$), the number of mobsters, numbered from $1$ to $n$.

The second line contains $n$ integers $s_1, s_2, \ldots, s_n$ ($1 \le s_i \le n$), separated by single spaces, where $s_i$ is the mobster that mobster $i$ aims at. Note that $s_i = i$ is allowed, meaning mobster $i$ aims at himself.

Print a single line with two integers separated by one space: the minimum and the maximum possible number of casualties.