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.
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
from fractions import gcd
import heapq
raw_input = stdin.readline
pr = stdout.write
mod=998244353

def ni():
    return int(raw_input())


def li():
    return list(map(int,raw_input().split()))


def pn(n):
    stdout.write(str(n)+'\n')


def pa(arr):
    pr(' '.join(map(str,arr))+'\n')

# fast read function for total integer input

def inp():
    # this function returns whole input of
    # space/line seperated integers 
    # Use Ctrl+D to flush stdin.
    return tuple(map(int,stdin.read().split()))
    
range = xrange # not for python 3.0+

# main code
"""
for t in range(ni()):
    n,m=li()
    c=0
    l=[]
    for i in range(n):
        x=li()
        l.append(x)
    for i in range(n):
        for j in range(m):
            if l[i][j] or (i>0 and l[i-1][j]) or (j>0 and l[i][j-1]) or (i<n-1 and l[i+1][j]) or (j<m-1 and l[i][j+1]):
                continue
            c+=1
        
    if c%2:
        pr('Ashish\n')
    else:
        pr('Vivek\n')
    
"""
for t in range(ni()):
    n=ni()
    l1=li()
    l2=li()
    x=l2.count(0)
    if x==n or x==0:
        if l1==sorted(l1):
            pr('Yes\n')
        else:
            pr('No\n')
    else:
        pr('Yes\n')
    
