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 : Shorya
#contact: shorya361@gmail.com
#Punk_GTS python Template
from sys import stdin,stdout
from collections import  Counter, defaultdict
import  math
def readInt(): return int(stdin.readline())
def readString(): return (stdin.readline())[:-1]
def readListInt(): return list(map(int,stdin.readline().split()))
def readListStr(): return list(map(str,stdin.readline().split()))
def nextLine(): stdout.write("\n")
def show(x): stdout.write(str(x) +"\n")
def showInline(x) : stdout.write(str(x))
def showList(x):
    for i in x:
        stdout.write(str(i)+" ")
    nextLine()
def show2D(x):
    for i in range(len(x)):
        for j in range(len(x[0])):
            stdout.write(str(x[i][j])+" ")
        nextLine()
def emptyList(length , value=-1): return [value]*length
def empty2D(row , col , val=-1) : return [ [val for i in range(col)] for j in range(row) ]
def isSquare(x):
    if ((x**(0.5))*10) % 10 ==0:
        return 1
    return 0
def isLog(val,base):
    a=math.log(val,base)
    if (a*10 )%10==0:
        return 1
    else:
        return 0
#-------------------------------------------------------------------------------------------------


def solve():
    #start coding
    for testcases in range(readInt()):
        n=readInt()
        a=readListInt()
        b=readListInt()
        a1=sorted(a)
        b1=sum(b)
        if a1==a or (b1!=0 and b1!=n):
            show("Yes")
        else:
            show("No")




solve()