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:
def swap(a, b, value_arr, type_arr):
    value_arr[a], value_arr[b] = value_arr[b], value_arr[a]
    type_arr[a], type_arr[b] = type_arr[b], type_arr[a]

def trouble_sort(start, value_arr, type_arr):
    if len(value_arr[start:]) <= 1 and len(type_arr[start:]) <= 1:
        return True
    min_value = min(value_arr[start:])
    min_index = value_arr.index(min_value)
    if min_index <= start:
        return trouble_sort(start + 1, value_arr, type_arr)
    min_type = type_arr[min_index]
    if type_arr[start] != min_type:
        swap(start, min_index, value_arr, type_arr)
        return trouble_sort(start + 1, value_arr, type_arr)
    else:
        try:
            alt_index = type_arr.index(1 - min_type)
        except ValueError:
            return False
        swap(start, alt_index, value_arr, type_arr)
        swap(start, min_index, value_arr, type_arr)
        swap(min_index, alt_index, value_arr, type_arr)
        return trouble_sort(start + 1, value_arr, type_arr)

for _ in range(int(input())):

    n = int(input())
    values = list(map(int, input().split()))
    types = list(map(int, input().split()))

    if trouble_sort(0, values, types) is True:
        print("Yes")
    else:
        print("No")