B'While searching for the pizza, baby Hosssam came across two permutations a and b of length n . Recall that a permutation 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). Baby Hosssam forgot about the pizza and started playing around with the two permutations. While he was playing with them, some elements of the first permutation got mixed up with some elements of the second permutation, and to his surprise those elements also formed a permutation of size n . Specifically, he mixed up the permutations to form a new array c in the following way. You know permutations a , b , and values at some positions in c . Please count the number different permutations c that are consistent with the described process and the given values. Since the answer can be large, print it modulo 10^9+7 . It is guaranteed that there exists at least one permutation c that satisfies all the requirements. The first line contains an integer t ( 1 <= t <= 10^5 ) -- the number of test cases. The first line of each test case contains a single integer n ( 1 <= n <= 10^5 ) -- the length of the permutations. The next line contains n distinct integers a_1,a_2, ldots,a_n ( 1 <= a_i <= n ) -- the first permutation. The next line contains n distinct integers b_1,b_2, ldots,b_n ( 1 <= b_i <= n ) -- the second permutation. The next line contains n distinct integers d_1,d_2, ldots,d_n ( d_i is either 0 , a_i , or b_i ) -- the description of the known values of c . If d_i=0 , then there are no requirements on the value of c_i . Otherwise, it is required that c_i=d_i . It is '...