CF1365B Trouble Sort

Ashish has $ n $ elements arranged in a line. These elements are represented by two integers $ a_i $ — the value of the element and $ b_i $ — the type of the element (there are only two possible types: $ 0 $ and $ 1 $ ). He wants to sort the elements in non-decreasing values of $ a_i $ . He can perform the following operation any number of times: - Select any two elements $ i $ and $ j $ such that $ b_i \ne b_j $ and swap them. That is, he can only swap two elements of different types in one move. Tell him if he can sort the elements in non-decreasing values of $ a_i $ after performing any number of operations.

The first line contains one integer $ t $ $ (1 \le t \le 100) $ — the number of test cases. The description of the test cases follows. The first line of each test case contains one integer $ n $ $ (1 \le n \le 500) $ — the size of the arrays. The second line contains $ n $ integers $ a_i $ $ (1 \le a_i \le 10^5) $ — the value of the $ i $ -th element. The third line containts $ n $ integers $ b_i $ $ (b_i \in \{0, 1\}) $ — the type of the $ i $ -th element.

For each test case, print "Yes" or "No" (without quotes) depending on whether it is possible to sort elements in non-decreasing order of their value. You may print each letter in any case (upper or lower).

For the first case: The elements are already in sorted order. For the second case: Ashish may first swap elements at positions $ 1 $ and $ 2 $ , then swap elements at positions $ 2 $ and $ 3 $ . For the third case: The elements are already in sorted order. For the fourth case: No swap operations may be performed as there is no pair of elements $ i $ and $ j $ such that $ b_i \ne b_j $ . The elements cannot be sorted. For the fifth case: Ashish may swap elements at positions $ 3 $ and $ 4 $ , then elements at positions $ 1 $ and $ 2 $ .