Problem: 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 ≠ 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.

Input

The first line contains one integer t (1 ≤ t ≤ 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 ≤ n ≤ 500) — the size of the arrays.

The second line contains n integers a_i (1 ≤ a_i ≤ 10^5) — the value of the i-th element.

The third line containts n integers b_i (b_i ∈ \{0, 1\}) — the type of the i-th element.

Output

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).

Example

Input


5
4
10 20 20 30
0 1 0 1
3
3 1 2
0 1 1
4
2 2 4 8
1 1 1 1
3
5 15 4
0 0 0
4
20 10 100 50
1 0 0 1


Output


Yes
Yes
Yes
No
Yes

Note

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 ≠ 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.

Solution (in JAVA):

Solution:
import java.util.*;

public class Solution {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in) ; 
		int t = sc.nextInt(); 
		while(t>0) {
			
			int n; 
			n = sc.nextInt() ; 
			int[][] arr = new int[n][2] ; 
			boolean isSorted = true ;
			int prev = Integer.MIN_VALUE ; 
			for(int i =0; i < n ; i++) {
				arr[i][0]  = sc.nextInt();  
				if( arr[i][0]<prev )isSorted=false ; 
				prev = arr[i][0] ; 
			}
			int z , o ; 
			z=o = 0 ; 
			
			for(int i =0; i < n ; i++) {
				arr[i][1] = sc.nextInt() ; 
				if( arr[i][1]==0 )z++ ; else o++ ; 
			}
			if(n==1) {
				System.out.println("Yes") ;
				t-- ; 
				continue ; 
			}
			
			
			if( (z==n   || o == n )  && !isSorted ) {
				System.out.println("No") ; 
			}
			else System.out.println("Yes") ; 
			
			t-- ; 
		}
	}
}