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:
# elemnts only of different b can change their position, so in a scenario with
# only one b and plenty of a, we can sort all elements of a using the ideia of
# selection sort. Using the same ideia, we can sort all elements with b = 1
# afterwards. The only case were isn't possible to sort is when all elements
# has the same b, in that case they must be already in ascending order.

# get number of test cases
testCases = int(input())

# for each test case
while testCases > 0:

    # read array size
    size = int(input())

    # read both arrays
    elements = list(map(int, input().split()))
    pairity = list(map(int, input().split()))

    # check if parity in unique
    zeroParity = False
    oneParity = False
    for b in pairity:
        if b == 0:
            zeroParity = True
        else:
            oneParity = True

    # both are true (since size >= 1, at least one will be true, so they can't
    #                be here both false)
    if zeroParity == oneParity:
        print('Yes')

    # array only with 0 or 1 -> elements must be sorted
    else:
        ordered = True
        for i in range(size - 1):
            if elements[i] > elements[i + 1]:
                ordered = False
                break

        # print response
        if ordered is True:
            print('Yes')
        else:
            print('No')

    # decrese test cases
    testCases -= 1