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 PYTHON3):

Solution:
import sys
import math
from  collections import defaultdict

# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')

def solve(test):
	n = int(input())
	a = list(map(int, input().split()))
	b = list(map(int, input().split()))
	if sorted(a) == a:
		print('Yes')
		return
	rec = [(a[i], b[i], i) for i in range(n)]
	rec.sort(key = lambda x: x[0])
	ones, zeros = 0, 0
	flag = 0
	flag2 = 0
	for i in range(n):
		if rec[i][1]:
			ones += i - rec[i][2]
			flag = 1
		else:
			zeros += i - rec[i][2]
			flag2 = 1

	print('Yes' if ones + zeros == 0 and flag and flag2 else 'No')



if __name__ == "__main__":
	test_cases = int(input())
	for t in range(1, test_cases + 1):
		solve(t)