You are given two arrays a1,a2,…,an and b1,b2,…,bn.In one operation, you can choose any integer i from 1 to n and swap the numbers ai and bi

.Determine whether, after using any (possibly zero) number of operations, the following two conditions can be satisfied simultaneously:

an=max(a1,a2,…,an),

bn=max(b1,b2,…,bn).

Here max(c1,c2,…,ck)

?denotes the maximum number among c1,c2,…,ck

. For example, max(3,5,4)=5, max(1,7,7)=7, max(6,2)=6

.Input

Each test contains multiple test cases. The first line contains the number of test cases t

?(1≤t≤200). The description of the test cases follows.

The first line of each test case contains a single integer n (1≤n≤100) — the length of the arrays.

The second line of each test case contains n integers a1,a2,…,an (1≤ai≤100) — elements of the first array.

The third line of each test case contains n integers b1,b2,…,bn (1≤bi≤100) — elements of the second array.

Output

For each test case, print "Yes" if after using any (possibly zero) number of operations the conditions described above are satisfied. Otherwise, print "No".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Example

input

7

3

7 9 7

7 6 9

4

10 10 15 15

10 16 15 15

2

100 99

99 100

1

1

1

9

1 2 3 4 5 6 7 8 9

9 9 9 9 9 9 6 6 6

7

1 1 2 2 1 1 2

1 2 1 2 1 2 1

2

30 4

5 30

output

Yes

No

Yes

Yes

Yes

No

No

Note

In the first test case, you can swap the numbers a3 and b3, after which the array a becomes equal to [7,9,9], and the array b becomes equal to [7,6,7], and both conditions are met.

In the second test case, it can be proved that it is impossible to satisfy both conditions.

In the third test case, you can swap the numbers a1 and b1, after which the array a

?becomes equal to [99,99], and the array b becomes equal to [100,100], and both conditions are satisfied.

In fifth test case, you can swap a7 and b7, a8 and b8, a9 and b9, after which the array a

?becomes equal to [1,2,3,4,5,6,6,6,6], and the array b becomes equal to [9,9,9,9,9,9,7,8,9]

, and both conditions are satisfied.

就是說給定2個數(shù)組，想確認能否通過交換數(shù)組對應(yīng)的位置，使得數(shù)組的最后1個數(shù)字就是這個數(shù)組的最大值，如果可以，輸出yes，如果不可以，輸出no；

思路是把所有對應(yīng)數(shù)字中小的數(shù)字放一個數(shù)組中，大的數(shù)字放到另一個數(shù)組中，去判斷最后一個數(shù)字是否是該數(shù)組的最大值，如果是則返回yes，不是則返回no

下面是代碼：