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.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {
    public static void main(String args[] ) throws Exception {
        Scanner sc = new Scanner(System.in);
        int t;
        t = sc.nextInt();
        int[] sizes = new int[t];
        String[] result = new String[t];
        int i,j,k;
        for(i=0;i<t;i++){
            sizes[i] = sc.nextInt();
            int[] a = new int[sizes[i]];
            int[] b = new int[sizes[i]];
            for(j=0;j<sizes[i];j++){
                a[j] = sc.nextInt();
            }
            for(k=0;k<sizes[i];k++){
                b[k] = sc.nextInt();
            }
            result[i] = evaluate(a, b);
        }

        for(i=0;i<t;i++){
            System.out.println(result[i]);
        }
        sc.close();
    }

    static String evaluate(int[] value, int[] type){
        int i, typeA=0, typeB=0;
        if(isSorted(value)){
            return "Yes";
        }

        for(i=0;i<type.length;i++){
            if(type[i] == 0)
                typeA++;
            if(type[i] == 1)
                typeB++;
        }

        if(typeA >= 1 && typeB >= 1)
            return "Yes";
        
        return "No";
    }

    static boolean isSorted(int[] value){
        for(int i=0, j = i+1; i<value.length-1; i++,j++){
            if(value[j]<value[i]){
                return false;
            }
        }
        return true;
    }
}

/*abstract

int min, i, j, temp, pos;
        for(i=0;i<value.length-1; i++){
            min = value[i];
            pos = i;
            for(j=i+1;j<value.length;j++){
                if(value[j]<min){
                    min = value[j];
                    pos = j;
                }
            }if(i==pos){
                continue;
            }else if(type[i]==type[pos]){
                return "No";
            }else if(type[i]!=type[pos]){
                temp = value[i];
                value[i] = value[pos];
                value[pos] = temp;
                
                temp = type[i];
                type[i] = type[pos];
                type[pos] = temp;
            }
        }
        
        return "Yes";

*/