Problem Description

In the Data structure class of HEU, the teacher asks one problem: How to find the longest path of one tree and the number of such longest path?

Input

There are several test cases. The first line of each case contains only one integer N, means there are N nodes in the tree. N-1 lines follow, each line has three integers w,v and len, indicate that there is one edge between node w and v., and the length of the edge is len.

Output

For each test case, output the length of longest path and its number in one line.

4
1 2 100
2 3 50
2 4 50
4
1 2 100
2 3 50
3 4 50

150 2
200 1