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;

public class TroubleSort {
	public static void main(String args[]) {
		try {
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

			int t = Integer.parseInt(br.readLine());

			while (t-- > 0) {
				int n = Integer.parseInt(br.readLine());
				String[] stra = br.readLine().split(" ");
				String[] strb = br.readLine().split(" ");

				int[] a = new int[n];
				int[] b = new int[n];

				for (int i = 0; i < n; i++) {
					a[i] = Integer.parseInt(stra[i]);
				}
				for (int i = 0; i < n; i++) {
					b[i] = Integer.parseInt(strb[i]);
				}
				
				if (isSorted(a)) {
					System.out.println("Yes");
					continue;
				}
				
				boolean temp = false;
				for (int i = 1; i < n; i++) {
					if (b[i] != b[i-1]) {
						temp = true;
						break;
					}
				}
				
				if (!temp) {
					System.out.println("No");
				}
				else {
					System.out.println("Yes");
				}
				
			}

		} catch (Exception e) {
			return;
		}
	}
	
	static boolean isSorted(int[] arr) {
		int len = arr.length;
		for (int i = 1; i < len; i++) {
			if (arr[i] < arr[i-1]) {
				return false;
			}
		}
		return true;
	}
	
}