Selecting Numbers

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Time limit1sMemory limit128 MB

Summary

Given a functional graph i->A_i on 1..N, find the maximum set of indices closed under this mapping (union of cycles) and print it.

Level: Medium4 of 10
Topics: Graph, Array, Implementation
Solved: No attempts yet

Problem

There is a table with 2 rows and N columns. The first row contains the integers from 1 to N in order. In the i-th cell of the second row, there is an integer A_i between 1 and N.

Choose some integers from the first row and let them form a set S. The values A_i directly below the chosen integers form another set T. The choice is valid when S and T are the same set.

Find a valid choice with maximum |S|, and output the chosen integers.

Input

The first line contains an integer N (1 <= N <= 100). The next N lines contain A_1, A_2, ..., A_N in order, one integer per line. Each A_i is between 1 and N.

Output

Print the number of chosen integers on the first line. Then print the chosen integers in increasing order, one per line.

Examples1

Example 1
Input
```
7
3
1
1
5
5
4
6
```
Expected output
```
3
1
3
5
```