B'You are given a tree with n vertices labeled from 1 to n . An integer a_{i} is written on vertex i for i = 1, 2, ldots, n . You want to make all a_{i} equal by performing some (possibly, zero) spells. Suppose you root the tree at some vertex. On each spell, you can select any vertex v and any non-negative integer c . Then for all vertices i in the subtree ^{ dagger} of v , replace a_{i} with a_{i} oplus c . The cost of this spell is s cdot c , where s is the number of vertices in the subtree. Here oplus denotes the bitwise XOR operation. Let m_r be the minimum possible total cost required to make all a_i equal, if vertex r is chosen as the root of the tree. Find m_{1}, m_{2}, ldots, m_{n} . ^{ dagger} Suppose vertex r is chosen as the root of the tree. Then vertex i belongs to the subtree of v if the simple path from i to r contains v . Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= t <= 10^{4} ). The description of the test cases follows. The first line of each test case contains a single integer n ( 1 <= n <= 2 cdot 10^{5} ). The second line of each test case contains n integers a_1, a_2, ldots, a_n ( 0 <= a_i < 2^{20} ). Each of the next n-1 lines contains two integers u and v ( 1 <= u, v <= n ), denoting that there is an edge connecting two vertices u and v . It is guaranteed that the given edges form a tree. It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^{5} . For each test case, print m_1, m_2, ldots, m_n on a new line. In the first test case, to find m_1 we root the tree at vertex 1 . Now all the values in array a are equal, and the total cost is 3 + 3 + 2 = 8 . The values m_2 , '...