D. MEX Treetime limit per test1.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a tree with n nodes, numerated from 0 to n-1. For each k between 0 and n, inclusive, you have to count the number of unordered pairs (u,v), u \neq v, such that the MEX of all the node labels in the shortest path from u to v (including end points) is k.The MEX of a sequence of integers is the smallest non-negative integer that does not belong to the sequence.InputThe first line contains a single integer t (1 \le t \le 10^4) — the number of test cases. The first line of each test case contains a single integer n (2 \le n \le 2 \cdot 10^{5}).The next n-1 lines of each test case describe the tree that has to be constructed. These lines contain two integers u and v (0 \le u,v \le n-1) denoting an edge between u and v (u \neq v).It is guaranteed that the given edges form a tree.It is also guaranteed that the sum of n for all test cases does not exceed 2 \cdot 10^{5}.OutputFor each test case, print n+1 integers: the number of paths in the tree, such that the MEX of all the node labels in that path is k for each k from 0 to n.ExampleInput
2
4
0 1
0 2
2 3
2
1 0
Output
1 2 1 1 1 
0 0 1 
Note  In example case 1,    For k = 0, there is 1 path that is from 2 to 3 as MEX([2, 3]) = 0.  For k = 1, there are 2 paths that is from 0 to 2 as MEX([0, 2]) = 1 and 0 to 3 as MEX([0, 2, 3]) = 1.  For k = 2, there is 1 path that is from 0 to 1 as MEX([0, 1]) = 2.  For k = 3, there is 1 path that is from 1 to 2 as MEX([1, 0, 2]) = 3  For k = 4, there is 1 path that is from 1 to 3 as MEX([1, 0, 2, 3]) = 4.   In example case 2,    For k = 0, there are no such paths.  For k = 1, there are no such paths.  For k = 2, there is 1 path that is from 0 to 1 as MEX([0, 1]) = 2.  
2
4
0 1
0 2
2 3
2
1 0

1 2 1 1 1  0 0 1  
['combinatorics', 'dfs and similar', 'implementation', 'math', 'trees', '*2400']