Ancestors in Two Trees

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You are given two rooted trees, each with N nodes. The nodes in each tree are labeled from 1 to N. The root of each tree is the node labeled 1 in that tree.
Your task is simple: For each i, find the number of j's (j ≠ i), such that node j is an ancestor of node i in both the trees.
Input
 The first line of the input contains an integer T denoting the number of test cases.
 First line of each testcase contains N, the number of nodes in each tree.
 The ith of the next N  1 lines contains two integers, u_{i} and v_{i}, which denotes that there is an edge between node u_{i} and node v_{i} in the first tree.
 The ith of the next N  1 lines contains two integers, u_{i} and v_{i}, which denotes that there is an edge between node u_{i} and node v_{i} in the second tree.
Output
For each test case, output a single line containing N integers, ith integer is the number of nodes which are ancestors of node i in both the trees.
Constraints
 1 ≤ T ≤ 10000
 2 ≤ N ≤ 500,000
 1 ≤ sum of N in all testcases ≤ 500,000
 1 ≤ u_{i}, v_{i} ≤ N
Example
Input: 1 5 1 3 1 2 3 5 3 4 1 5 1 2 2 3 3 4 Output: 0 1 1 2 1
Explanation
Because node 1 is the root in both the trees, there is no node above them. So first output is 0.
Node 1 is the only node which is an ancestor of Node 2 in both the trees. So the second output is 1.
Node 1 is the only node which is an ancestor of Node 3 in both the trees. So the third output is 1.
Node 1 and node 3 are the only nodes which are ancestors of Node 4 in both the trees. So the fourth output is 2.
Node 1 is the only node which is an ancestor of Node 5 in both the trees. So the fifth output is 1.
Author:  kingofnumbers 
Tags  kingofnumbers 
Date Added:  1062017 
Time Limit:  3 sec 
Source Limit:  50000 Bytes 
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