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:
from collections import Counter
from sys import stdin
t = int(input())

result = ""
res_table = {False: "No", True: "Yes"}

for _ in range(t):

    def check_ascending(both):

        for i in range(len(both) - 1):

            if both[i] > both[i +1]:

                return False
        
        return True

    n =  int(input())

    vals = [int(i) for i in stdin.readline().split()]
    types = [int(i) for i in stdin.readline().split()]
    both =  [(i,j) for i,j in zip(vals, types)]


    # type0 = []
    # indices0 = []
    # type1 = []
    # indices1 = []
    # i = 0
    # for val, typ in zip(vals, types):

    #     if typ == 0:
    #         type0.append(val)
    #         indices0.append(i)
    #     else:
    #         type1.append(val)
    #         indices1.append(i)

    #     i += 1
    

    # type0.sort()
    # type0  = [(val, i) for val,i in zip(type0, indices0)]
    # type1.sort()
    # type1  = [(val, i) for val,i in zip(type1, indices1)]

    # print(type0, type1)

    # i = i0 = i1 = 0
    # flag = True
    # while i0 < len(type0) and i1 < len(type1):

    #     val0, index0 = type0[i0]
    #     val1, index1 = type1[i1]

    #     if index0 < index1 and val0 <= val1:

    #         i0 += 1
        
    #     elif index1 < index0 and val1 <= val0:

    #         i1 += 1
        
    #     else:
    #         flag =  False
    #         break

    #     i += 1
    
    # print(flag)

    # for i in range(len(both) - 1):

    #     for j in range(0, len(both) - i - 1):


    #         if both[j][0] > both[j+1][0] or both[j][1] != both[j+1][1]: 
    #             both[j], both[j+1] = both[j+1], both[j]
    
    
    # result += res_table[(check_ascending(both))] + "\n"

    flag = False
    counter = Counter(types)
    if 1 in counter and 0 in counter:

        flag = True
    
    elif check_ascending(vals):

        flag = True

    result += res_table[flag] + "\n"

    

    
print(result[:-1])