write a go solution for F1. Chain Prefix Rank (Easy Version)time limit per test5 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard output  This is the easy version of the problem. The difference between the versions is that in this version, n<=5000. You can hack only if you solved all versions of this problem. Given a tree T with n vertices rooted at 1 and a sequence a of length n, count the number of permutations^∗ p of length n that satisfy the following condition:  For all 1<=u<=n, there are exactly a_u vertices v such that v is an ancestor of u in T and p_v<p_u. Output the answer modulo 998,244,353. Input data is selected in such a way that at least one valid permutation exists.^∗A permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array), and [1,3,4] is also not a permutation (n=3 but there is 4 in the array). InputEach test contains multiple test cases. The first line contains the number of test cases t (1<=t<=2500). The description of the test cases follows. The first line of each test case contains an integer n (2<=n<=5000) — the number of vertices.The second line of each test case contains n-1 integers fa_2,fa_3,ldots,fa_n (1<=fa_i<i)— fa_i is the parent of i on T.The third line of each test case contains n integers a_1,a_2,ldots,a_n (0<=a_i<n).It is guaranteed that the sum of n over all test cases does not exceed 5000. Input data is selected in such a way that at least one valid permutation exists.OutputFor each test case, output one integer — the number of permutations modulo 998,244,353.ExampleInput351 2 3 40 1 2 3 451 2 1 10 1 0 0 081 1 3 3 4 5 70 0 1 0 1 3 3 1Output164NoteVisualizer linkIn the first test case, the only permutation which satisfies the condition is [1,2,3,4,5].In the second test case, permutations which satisfy the condition are [4,5,1,2,3],[4,5,1,3,2],[4,5,2,1,3],[4,5,2,3,1],[4,5,3,1,2],[4,5,3,2,1].In the third test case, permutations which satisfy the condition are [3,1,6,2,5,7,8,4],[3,1,6,2,5,8,7,4],[3,2,6,1,5,7,8,4],[3,2,6,1,5,8,7,4].. Output only the code with no comments, explanation, or additional text.