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(1000000) #设置最大递归深度
int1 = lambda x: int(x) - 1 #返回x-1
p2D = lambda x: print(*x, sep="\n") #输出多个元素，以换行符分割
p2S = lambda x: print(*x, sep=" ") #输出多个元素，以空格分割
def II(): return int(sys.stdin.readline()) #读一行（仅一个）整数
def MI(): return map(int, sys.stdin.readline().split()) #读一行数据，转化为int型元组
def LI(): return list(map(int, sys.stdin.readline().split())) #读一行数据，转化为int型列表
def LLI(rows_number): return [LI() for _ in range(rows_number)] 
def SI(): return sys.stdin.readline()[:-1] #读一行字符串，舍掉换行符



def main():
    _v_ = II()
    for _ in range(_v_):
        n = II()
        ins = LI()
        s = LI()
        a, b = False, False
        c = True
        for i in s:
            if i == 0:
                a = True
            else:
                b = True
        ins1 = ins[0]
        for i in ins:
            if ins1 > i:
                c = False
                break
            ins1 = i
        if (a == True and b == True) or c == True:
            print('Yes')
        else:
            print('No')
        

        

        

                 
main()