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 PYTHON):

Solution:
from collections import defaultdict, Counter
from math import log, ceil

import sys

#sys.stdin = open("second.txt", "r")
raw_input = sys.stdin.readline

t = int(raw_input())
for t_itr in xrange(t):
	n = int(raw_input())
	a = map(int, raw_input().split())
	b = map(int, raw_input().split())


	#Regroupement
	type_1 = []
	type_2 = []
	for n_itr in xrange(n):
		if b[n_itr] == 0:
			type_1.append(a[n_itr])
		else:
			type_2.append(a[n_itr])

	if type_1 and type_2:
		print "Yes"
	else:
		if type_1 and not type_2:
			tmp = type_1
		else:
			tmp = type_2
		test = True
		for n_itr in xrange(1, n):
			if tmp[n_itr] < tmp[n_itr - 1]:
				test = False
				break
		if test == True:
			print 'Yes'
		else:
			print 'No'