Anagram

problem

Given a sequence $a_i$ of length $N$. Output all integers $K (1 \ le K \ le N)$ that satisfy the following conditions.

Condition: Well sorted $a_1, \ cdots, a_K$ matches $a_ {N-K + 1}, \ cdots, a_N$.

Example

Input

8 5 2 4 9 4 9 2 5

Output

1 2 4 6 7 8

inputFormat

outputFormat

Output all integers $K (1 \ le K \ le N)$ that satisfy the following conditions.

Condition: Well sorted $a_1, \ cdots, a_K$ matches $a_ {N-K + 1}, \ cdots, a_N$.

Example

Input

8 5 2 4 9 4 9 2 5

Output

1 2 4 6 7 8

样例

8
5 2 4 9 4 9 2 5

1 2 4 6 7 8