B'Note the unusual definition of text{MEX} in this problem. Piggy gave Turtle a binary tree ^{ dagger} with n vertices and a sequence a_1, a_2, ldots, a_n on his birthday. The binary tree is rooted at vertex 1 . If a set of paths P = {(x_i, y_i) } in the tree covers each edge exactly once, then Turtle will think that the set of paths is good. Note that a good set of paths can cover a vertex twice or more. Turtle defines the value of a set of paths as sum limits_{(x, y) in P} f(x, y) , where f(x, y) denotes the text{MEX}^{ ddagger} of all a_u such that vertex u is on the simple path from x to y in the tree (including the starting vertex x and the ending vertex y ). Turtle wonders the minimum value over all good sets of paths. Please help him calculate the answer! ^{ dagger} A binary tree is a tree where every non-leaf vertex has at most 2 sons. ^{ ddagger} text{MEX} of a collection of integers c_1, c_2, ldots, c_k is defined as the smallest positive integer x which does not occur in the collection c . For example, text{MEX} of [3, 3, 1, 4] is 2 , text{MEX} of [2, 3] is 1 . 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 ( 2 <= n <= 2.5 cdot 10^4 ) -- the number of vertices in the tree. The second line of each test case contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= 10^9 ) -- the elements of the sequence a . The third line of each test case contains n - 1 integers p_2, p_3, ldots, p_n ( 1 <= p_i < i ) -- the parent of each vertex in the tree. Additional constraint on the input: the given tree is a binary tree, that is, every non-leaf vertex has at most 2 '...