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1257 - Farthest Nodes in a Tree (II)
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Time Limit: 2 second(s) Memory Limit: 32 MB

Given a tree (a connected graph with no cycles), you have to find the cost to go to the farthest node from each node. The edges of the tree are weighted and undirected.

Input

Input starts with an integer T (≤ 10), denoting the number of test cases.

Each case starts with an integer n (2 ≤ n ≤ 30000) denoting the total number of nodes in the tree. The nodes are numbered from 0 to n-1. Each of the next n-1 lines will contain three integers u v w (0 ≤ u, v < n, u ≠ v, 1 ≤ w ≤ 10000) denoting that node u and v are connected by an edge whose weight is w. You can assume that the input will form a valid tree.

Output

For each case, print the case number in a line first. Then for each node (from 0 to n - 1) print the cost to go to the farthest node in a separate line.

Sample Input

Output for Sample Input

2

4

0 1 20

1 2 30

2 3 50

5

0 2 20

2 1 10

0 3 29

0 4 50

Case 1:

100

80

50

100

Case 2:

50

80

70

79

80

Note

Dataset is huge, use faster I/O methods.


Problem Setter: Jane Alam Jan
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