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

input = sys.stdin.readline


for _ in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))

    if sorted(a) == a:
        print('Yes')
        continue

    if 0 in b and 1 in b:
        print('Yes')
    else:
        print('No')


# for i in range(int(input())):
#     n, m = map(int, input().split())
#     l = list()
#     l_block = set()
#     ans = True
#
#     for i in range(n):
#         line = input().strip()
#         s = []
#
#
#
#         n = False
#
#         for j, c in enumerate(line.strip()):
#             s.append(c)
#             if c == 'B':
#                 if j:
#                     if s[j - 1] == 'G':
#                         ans = False
#                     s[j - 1] = '#'
#                 if i:
#                     if l[i-1][j] == 'G':
#                         ans = False
#                     l[i-1][j] = '#'
#                 n = True
#                 l_block.add(j)
#
#             elif n == True:
#                 if s[j] == 'G':
#                     ans = False
#                 s[j] = '#'
#
#         for c in l_block:
#             if s[c] == 'G':
#                 ans = False
#             s[c] = '#'
#
#         l_block = set()
#         l.append(s)
#
#     for li in l:
#         print(li)
#



# for _ in range(int(input())):
#     n = int(input())
#     a = map(int, input().split())
#     b = map(int, input().split())
#
#
#
#     if True:
#         print('Yes')
#     else:
#         print('No')
#

'''
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


'''