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

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

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

Examples