Call forwarding chaos

Dohun's unit has phones with a feature called call forwarding. Call forwarding sends an incoming call on one phone to another phone instead. For example, if phone $A$ forwards to phone $B$, a call to phone $A$ rings phone $B$. Each phone can forward to at most one other phone.

This feature has a serious flaw. When forwarding settings form a loop, some phones go dead. For example, phone $A$ forwards to phone $B$, phone $B$ forwards to phone $C$, and phone $C$ forwards to phone $A$. Then a call to any of the three phones waits forever, and all three phones go dead.

Impressed by this, Dohun plans to change the forwarding settings of some phones so that every phone in the unit goes dead. The unit has $N$ phones numbered $1$ to $N$. Phone $i$ currently forwards to phone $a_i$. If $a_i = i$, phone $i$ has no forwarding.

Changing too many settings would get Dohun caught by an officer, so he must change as few phones as possible. Find the minimum number of phones whose settings must change, along with the new settings. If several answers exist, any one is accepted. It is always possible to make every phone go dead.

The first line contains $N$, the number of phones. ($2\leq N\leq 100\,000$)

The second line contains $N$ integers $a_1, \cdots, a_N$ separated by spaces. ($1\leq a_i\leq N$)

If $a_i = i$, phone $i$ has no call forwarding.

The first line contains the minimum number of phones whose forwarding settings must change so that every phone goes dead.

The second line contains $N$ integers $b_1, \cdots, b_N$, the forwarding settings after the changes. If several answers exist, print any of them.