Given a tree of ~N~ nodes labeled from ~0~ to ~N - 1~, find out the minimum rooted tree among possible rooted trees

Input

• The first line is an integer ~N~ ~(1 \le N \le 10^5)~.
• Each line among the next ~N - 1~ lines contain ~2~ integers ~u, v~, the connecting edge between vertex ~u~ and vertex ~v~.

Output

• Print out the root node and the minimum tree height. If there are more than one possible root, print out the minimum node.

• Sample Input

7
0 1
1 2
2 3
3 5
3 4
4 6

Sammple Output

2 3