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:
#8:47
MOD=10**9+7
INT_MAX=10**20+7
def INPUT():return list(int(i) for i in input().split())
def LIST_1D_ARRAY(n):return [0 for _ in range(n)]
def LIST_2D_ARRAY(m,n):return [[0 for _ in range(n)]for _ in range(m)]
def power(a,x):
    res=1
    while(x>0):
        if x&1:
            res=(res*a)%MOD
        a=(a*a)%MOD
        x//=2
    return res%MOD
def NCR_MOD(n,r):
    num=1
    for i in range(n,n-r,-1):num=(num*i)%MOD
    for j in range(1,r+1):num=(num*power(j,MOD-2))%MOD
    return num
import math
from collections import deque
#################################################################################
def calc(n,val,type):
    x=LIST_1D_ARRAY(n)
    for i in range(n):
        x[i]=val[i]
    x.sort()
    if x==val:
        return True
    sum=0
    for i in range(n):
        sum+=type[i]
    if sum==0 or sum==n:
        return False
    return True



for i in range(int(input())):
    n=int(input())
    val=INPUT()
    type=INPUT()
    if calc(n,val,type):
        print("YES")
    else:
        print("NO")
    print()