Given a tree containing ~N~ nodes, print the maximum depth of the tree if the tree can be rooted at any node.

The maximum depth of a tree rooted at a certain node ~u~ is defined as the maximal number of edges in the path that begins at ~u~.

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 10^5)~, the number of nodes.

The next ~N-1~ lines will each contain ~2~ integers, ~a, b~ ~(1 \le a, b \le N)~, indicating nodes ~a~ and ~b~ are connected by a single edge. It is guaranteed the entire tree is connected.

Output Specification

On the first line, output ~2~ integers, the maximum depth of the tree, and the node to root the tree at. If there are multiple such nodes, print the one with the smallest index.

Sample Input

5
2 1
1 3
1 4
3 5

Sample Output

3 2

Explanation for Sample

If the tree was rooted at node ~2~, the maximum depth would be ~3~.