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

max_int = 1000000001  # 10^9+1
min_int = -max_int

t = int(input())
for _t in range(t):
    n = int(sys.stdin.readline())
    a = map(int, sys.stdin.readline().split())
    b = sys.stdin.readline().split()

    prev_zero = prev_one = 0
    zero_sorted = True
    ones_sorted = True
    has_zero = has_one = False

    for num, elem in enumerate(a):
        if b[num] == '0':
            has_zero = True

            if zero_sorted:
                if elem < prev_zero:
                    zero_sorted = False
                else:
                    prev_zero = elem
        else:
            has_one = True

            if ones_sorted:
                if elem < prev_one:
                    ones_sorted = False
                else:
                    prev_one = elem

    if has_one and has_zero:
        print('Yes')
    elif has_one:
        if ones_sorted:
            print('Yes')
        else:
            print('No')
    else:
        if zero_sorted:
            print('Yes')
        else:
            print('No')