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 sys import *


def solve(b):
    c1, c2 = 0, 0
    for el in b:
        if(el == 1):
            c1 += 1
        else:
            c2 += 1
    if(c1 == 0 or c2 == 0):
        print('No')
    else:
        print('Yes')
    pass


test = 1
test = int(input())
for t in range(0, test):
    # brr = [list(map(int,input().split())) for i in range(rows)]              # 2D array row-wise input
    n = int(input())
    # n, x = list(map(int, input().split()))
    brr = [int(x) for x in input().split()]
    arr = [int(x) for x in input().split()]
    if(brr==sorted(brr)):
        print('Yes')
    else:
        ans = solve(arr)


'''
rows, cols = (5, 5)
arr = [[0]*cols for j in range(rows)]                                         # 2D array initialization
b=input().split()                                                             # list created by spliting about spaces
brr = [[int(b[cols*i+j]) for j in range(cols)] for i in range(rows)]          # 2D array Linear Input
rows,cols=len(brr),len(brr[0])                                                # no of rows/cols for 2D array
arr.sort(key = lambda x : x[1])                                               # sort list of tuples by 2nd element, Default priority - 1st Element then 2nd Element
s=set()                                                                       # empty set
a=maxsize                                                                     # initializing infinity
b=-maxsize                                                                    # initializing -infinity
mapped=list(map(function,input))                                              # to apply function to list element-wise
try:                                                                          # Error handling
    #code 1
except:                                                                       # ex. to stop at EOF
    #code 2 , if error occurs
'''