Justified Jungle

As you probably know, a tree is a graph consisting of $n$ nodes and $n-1$ undirected edges in which any two nodes are connected by exactly one path. A forest is a graph consisting of one or more trees. In other words, a graph is a forest if every connected component is a tree. A forest is justified if all connected components have the same number of nodes.

Given a tree $G$ consisting of $n$ nodes, find all positive integers $k$ such that a justified forest can be obtained by erasing exactly $k$ edges from $G$. Note that erasing an edge never erases any nodes. In particular when we erase all $n-1$ edges from $G$, we obtain a justified forest consisting of $n$ one-node components.

Input

The first line contains an integer $n(2\le n\le 10^6)$ — the number of nodes in $G$. The $k$-th of the following $n-1$ lines contains two different integers $a_k$ and $b_k(1\le a_k,b_k\le n)$ — the endpoints of the $k$-th edge.

Output

Print in one line all wanted integers $k$, in increasing order.

Examples

Figures depict justified forests obtained by erasing $1,3$ and $7$ edges from the tree in the example input.