The Whisper Game

Problem Description

There are $n$ people numbered $1$ to $n$. Each person has a fixed whisper target: person $i$ will pass a message to person $a_i$ ($a_i$ may equal $i$).

The game rules are as follows. Each round is started by some person $x$. Person $x$ says to $a_x$ a string Oww...wwf containing $t$ letters w; if $t > 1$, then $a_x$ says to $a_{a_x}$ a string of the same form containing $t - 1$ letters w; and so on, until someone hears a string with exactly one w, namely Owf — that person is the receiver of this round. (At any moment, at most one round is in progress.)

Find the smallest $t$ ($t \geq 1$) such that for every person $x$ the following holds: if a round started by $x$ has receiver $y$, then a round started by $y$ must have receiver $x$. If no such $t$ exists, output $-1$.

Input Format

The first line contains an integer $n$ ($1 \le n \le 150$): the number of people.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$, where the $i$-th number is the whisper target $a_i$ of person $i$.

Output Format

Output the smallest $t$; if none exists, output $-1$.

Sample Input

4
2 3 1 4

Sample Output

3