There is a directed graph with 

N vertices and N edges.

The i-th edge goes from vertex i to vertex Ai. (The constraints guarantee that i！=A i.)

Find a directed cycle without the same vertex appearing multiple times.

It can be shown that a solution exists under the constraints of this problem.

Notes

The sequence of vertices B=(B1,B2 ,…,BM ) is called a directed cycle when all of the following conditions are satisfied:

1,M≥2

2,The edge from vertex Bi to vertex Bi+1exists. (1≤i≤M−1)

3,The edge from vertex BM  to vertex  exists.

4,If i!=j, then Bi!=Bj.

Constraints

All input values are integers.

2≤N≤2×10^5

1≤Ai≤N,Ai!=i

The input is given from Standard Input in the following format:

N

A1,A2...AN

Print a solution in the following format:

M

B1,B2....BN

M is the number of vertices, and Bi is the i-th vertex in the directed cycle.

The following conditions must be satisfied:

2≤M

B_i+1=A_Bi( 1≤i≤M−1 )

B_1=A_BM

Bi!=Bj(i!=j)

If multiple solutions exist, any of them will be accepted.

1

2

3