Given a tree ~N~ vertices, numbered from ~0~ to ~N-1~. Find the vertex with the smallest index such that the height of the tree is greatest if the vertex  with the smallest is root

Input

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

Output

• Print the vertex and maximum height

Example Input 1

3
0 1
1 2

Example Output 1

0 2

Example Input 2

4
0 1
0 2
2 3

Example Output 2

1 3