Competitions

# April 17 Graphs contest

# Center of the tree

Tree is given. Find its vertices for which the maximum of the distances to the remaining vertices of the tree will be minimal.

## Input data

First line contains number of vertices \:(1 \le n \le 30000) in the tree. The other n - 1 lines describe the tree. Line i contains vertex number — the parent of the vertex i. Vertex with number 1 is a root of the tree.

## Output data

Print the numbers of all the required vertices in ascending order.

## Examples

Input example #1

9 1 2 2 4 4 3 3 8

Output example #1

2 3