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:
"""
~~ Author : Bhaskar
~~ Dated : 07~06~2020
"""

import sys
from bisect import *
from math import floor,sqrt,ceil,factorial as F,gcd,pi,log
from itertools import chain,combinations,permutations,accumulate
from collections import Counter,defaultdict,OrderedDict,deque
from array import array
INT_MAX = sys.maxsize
INT_MIN = -(sys.maxsize)-1
mod = 1000000007
ch = "abcdefghijklmnopqrstuvwxyz"
lcm = lambda a,b : (a*b)//gcd(a,b)
setbit = lambda x : bin(x)[2:].count("1")

def solve():
    T = int(sys.stdin.readline())
    for _ in range(T):
        n = int(sys.stdin.readline())
        a = list(map(int,sys.stdin.readline().split()))
        b = list(map(int,sys.stdin.readline().split()))
        one = []
        zero = []
        for i in range(n):
            if b[i] == 1:
                one.append(a[i])
            else:
                zero.append(a[i])
        # print(one)
        # print(zero)
        if len(one) == 0:
            if zero == sorted(zero):
                print('Yes')
            else:
                print("No")
        elif len(zero) == 0:
            if one == sorted(one):
                print("Yes")
            else:
                print("No")
        else:
            print("Yes")


if __name__ == "__main__":
    try:
        sys.stdin = open("input.txt","r")
    except :
        pass
    solve()