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.Arrays;
import java.util.Scanner;

public class Main {
	static boolean check(int or[],int copy[]) {
		for(int i=0;i<or.length;i++) {
			if(or[i]!=copy[i]) {
				return false;
			}
		}
		return true;
	}
	static void swap(int tp[],int i,int j,int or[] ) {
		int temp=tp[i];
		int champ=or[i];
		tp[i]=tp[j];
		tp[j]=temp;
		or[i]=or[j];
		or[j]=champ;
	}
public static void main(String[] args) {
	Scanner o=new Scanner (System.in);
	int t=o.nextInt();
	while(t>0) {
			int n=o.nextInt();
			int ar[]=new int[n];
			for(int i=0;i<n;i++) {
				ar[i]=o.nextInt();
			}
			int tp[]=new int[n];
			for(int i=0;i<n;i++) {
				tp[i]=o.nextInt();
			}
			int tcopy[]=Arrays.copyOf(tp,n);
			int copy[]=Arrays.copyOf(ar, n);
			for(int i=0;i<n-1;i++) {
				Arrays.sort(copy);
			}
			if(check(ar,copy)) {
				System.out.println("Yes");
			}
			else {
				int co=0;
				int cz=0;
			for(int i=0;i<n;i++) {
				if(tp[i]==1)
					co++;
				else
					cz++;
			}
			if(cz>0&&co>0) {
				System.out.println("Yes");
			}
			else
				System.out.println("No");
			
			}
		t--;
	}	
}
	}