B"After (finally) qualifying for the IOI 2023, wxhtzdy was very happy, so he decided to do what most competitive programmers do: trying to guess the problems that will be on IOI. During this process, he accidentally made a problem, which he thought was really cool. You are given a tree (a connected acyclic graph) with n vertices and n-1 edges. Vertex i ( 1 <= i <= n ) has a value a_i . Lets' define g(u, v) as the bitwise or of the values of all vertices on the shortest path from u to v . For example, let's say that we want to calculate g(3, 4) , on the tree from the first test case in the example. On the path from 3 to 4 are vertices 3 , 1 , 4 . Then, g(3, 4) = a_3 | a_1 | a_4 (here, | represents the bitwise OR operation). Also, you are given q queries, and each query looks like this: You are given x and y . Let's consider all vertices z such that z is on the shortest path from x to y (inclusive). Lets define the niceness of a vertex z as the sum of the number of non-zero bits in g(x, z) and the number of non-zero bits in g(y, z) . You need to find the maximum niceness among all vertices z on the shortest path from x to y . Since his brain is really tired after solving an output only problem on SIO (he had to do it to qualify for the IOI), he wants your help with this problem. The first line of input contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The first line of each test case contains a single integer n ( 1 <= n <= 2 cdot 10^5 ) -- the number of vertices. The second line of each test case contains n positive integers a_1, a_2, ... , a_n ( 1 <= a_v <= 10^9 ) -- the value of each vertex, the i -th integer in this line corresponds to the vertex i . Following n - 1 lines are the description of a"...