## #1448 Tree Median

18  3 s   128 MB

## Description

A tree is a connected graph containing no cycles. A vertex is called a median vertex if the total cost to reach all vertices is minimal. There could be more than one median vertex in a tree, that’s why we define median as the set of all median vertices. To find median in a tree with small number of vertices is fairly easy task as you can solve this by a simple brute force program.

In the left figure, we can see a weighted tree with 5 vertices. The tree median is {B} because the total cost from vertex B to all other vertices is minimal.

B-A = 2    B-D = 7
B-C = 1    B-E = 7 + 5 = 12

TOTAL = 2 + 1 + 7 + 12 = 22


What if the number of vertices is quite large? This might be a problem since brute force program cost too much time. Given a weighted tree with N vertices, output the total cost to reach all vertices from its median.

## Input

Input consists of several cases. Each case begins with an integer n (1<= n <= 10,000) denoting the number of vertices in a tree. Each vertex is numbered from 0...n-1. Each of the next n-1 lines contains three integers: ab, and w (1<= w <= 100), which means a and b is connected by an edge with weight w.

Input is terminated when n is equal to 0. This input should not be processed.

## Output

For each case, output a line containing the sum of cost of path to all other vertices from the tree median.

### Sample Output

5
0 1 2
1 2 1
1 3 7
3 4 5
6
0 1 1
1 2 4
2 3 1
3 4 4
4 5 1
0
22
21