Play with Trees

You are given an unweighted, undirected tree T. We say T is special iff it has this property:

"All nodes of degree greater than or equal to 3 are surrounded by at most two nodes of degree two or greater."

Finding maximal size subtree of this tree so that it's a special tree.

Input

The first line of the input file contains one integer N --- number of nodes in the tree (0 < N <= 10⁶). Next N-1 lines contain N-1 edges of that tree --- Each line contains a pair (u, v) means there is an edge between node u and node v (1 <= u, v <= N).

Output

At the first line, output number of nodes in the optimal subtree you found. Next lines, print all edges belong to that subtree, each line contains a pair u v means an edge between node u and node v.

Example

Input:
5
1 2
2 3
2 4
2 5

Output:
5
1 2
2 3
2 4
2 5