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.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class TroubleSort {
	
	public static void main(String[] args) {
		try {						
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			int casos = Integer.parseInt(br.readLine());
			while(casos-- > 0) {				
				int valores = Integer.parseInt(br.readLine());
				StringTokenizer st = new StringTokenizer(br.readLine());
				if(leerValores(valores, st)){
					System.out.println("Yes");
					br.readLine();
				}else {
					st = new StringTokenizer(br.readLine());	
					if(leerBits(valores, st)) {
						System.out.println("Yes");						
					}else {
						System.out.println("No");
					}
				}
			}
			br.close();
		} catch (Exception e) {
			e.printStackTrace();
		}
	}

	private static boolean leerBits(int valores, StringTokenizer st) {
		boolean uno = false;
		boolean cero = false;
		for(int i=0; i<valores; i++) {
			int bit = Integer.parseInt(st.nextToken());
			if(bit == 0) {
				cero = true;
			}else {
				uno = true;
			}
			if(uno && cero) {
				return true;
			}
		}		
		return false;
	}

	private static boolean leerValores(int valores, StringTokenizer st) {
		int numeroAnterior = 0;
		for(int i=0; i<valores; i++) {
			int nuevoNum = Integer.parseInt(st.nextToken());
			if(nuevoNum >= numeroAnterior) {
				numeroAnterior = nuevoNum ;
			}else {
				return false;
			}
		}
		return true;
	}
}