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
import math
# sys.setrecursionlimit(10**6)

def get_ints(): return map(int, input().strip().split())
def get_list(): return list(get_ints())

def printspx(*args): return print(*args, end="")
def printsp(*args): return print(*args, end=" ")
def printchk(*args): return print(*args, end=" \ ")

MODPRIME = int(1e9+7); BABYMODPR = 998244353;


# sys.stdin = open("input.txt","r")  # <<<  Comment this line  >>> #
from collections import Counter
for _testcases_ in range(int(input())):
    n = int(input())
    a = get_list()
    b = get_list()
    li = list()
    # d = Counter(a)
    for i in range(n):
        li.append([a[i], b[i]])
    sorted_list = li.copy()
    sorted_list.sort(key = lambda x: x[0])
    flag = True; one = False; zero = False;
    same = diff = 0

    for i in range(n):
        if sorted_list[i][0] != li[i][0]:
            flag = False
        if li[i][1] == 0:
            zero = True
        elif li[i][1] == 1:
            one = True
    if flag:
        print("Yes")
    else:
        if one and zero:
            print("Yes")
        else:
            print("No")
    
'''
THE LOGIC AND APPROACH IS BY ME @luctivud ( UDIT GUPTA )
SOME PARTS OF THE CODE HAS BEEN TAKEN FROM WEBSITES LIKE::
(I Own the code if no link is provided here or I may have missed mentioning it)
>>> DO NOT PLAGIARISE.
TESTCASES:
>>> COMMENT THE STDIN !!
'''