Zenyk and the Martian permutation

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Zenyk received a Martian permutation \(p\) of numbers from 1 to \(n\) as a gift from Ilona.

A number \(k\) is called good if Zenyk can sort the given permutation by performing the following operation any number of times: choose \(i\) and swap \(p_i\) and \(p_{i + k}\).

Help Zenyk determine all positive integers that are good.

Input

The first line contains an integer \(n\) — the size of the permutation.

The second line contains \(n\) integers \(p_i\) — the permutation.

Output

In the first line, print an integer \(m\) — the number of good numbers.

In the second line, print \(m\) integers — the good numbers in ascending order.

Constraints

\(2 \le n \le 10^5\),

\(1 \le p_i \le n\),

there exists an index \(i\) such that \(p_i \neq i\),

for 60% of the tests, an additional constraint holds: \(n \le 2000\).

Samples