1428 - Tree Problem

Time Limit : 10 Second

Memory Limit : 128 MB

Submission: 312

Solved: 193

Description


A tree structure is very special structure, there is exactly one path connecting each pair of nodes.



Now, given a tree structure, which has N nodes(conveniently labeled from 1 to N). And the root of the tree is always labeled with 1. You are to write a program to figure out that, for every node V in the tree, how many nodes there are in the sub-tree rooted by V and it’s label number is larger than the label number of V.





For the example above:



Ans[1] = 6



Ans[2] = 1



Ans[3] = 2



Ans[4] = 0



Ans[5] = 0



Ans[6] = 0



Ans[7] = 0


Input


There are multiple cases.



The first line is an integer T representing the number of test cases.



The following T lines each line representing a test case. For each case there are exactly two lines:



The first line with a single integer N(1 <= N <= 50000), representing the size of tree.



The second line with N – 1 numbers: P[2], P[3], ……P[n]. (1 <= P[i] <= N)



 



It is guaranteed that the input data is a tree structure and has 1 as root.


Output


For each test case, output a line of N numbers in the following format:



Case #K: Ans[1] Ans[2] Ans[3] …… Ans[N].


sample input
2
7
1 1 3 2 1 3
4
1 2 3
sample output
Case #1: 6 1 2 0 0 0
Case #2: 3 2 1 0
hint

source
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