B. Trouble Sort
constructive algorithms; implementation
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 \(2\).