Showstopper
Contest: Codeforces Round 860 (Div. 2)
Difficulty rating: 800
Tags: greedy, implementation, sortings

You are given two arrays $$$a_1, a_2, \ldots, a_n$$$ and $$$b_1, b_2, \ldots, b_n$$$.

In one operation, you can choose any integer $$$i$$$ from $$$1$$$ to $$$n$$$ and swap the numbers $$$a_i$$$ and $$$b_i$$$.

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

- $$$a_n = \max(a_1, a_2, \ldots, a_n)$$$,
- $$$b_n = \max(b_1, b_2, \ldots, b_n)$$$.

Here $$$\max(c_1, c_2, \ldots, c_k)$$$ denotes the maximum number among $$$c_1, c_2, \ldots, c_k$$$. For example, $$$\max(3, 5, 4) = 5$$$, $$$\max(1, 7, 7) = 7$$$, $$$\max(6, 2) = 6$$$.

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

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

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 100$$$) — elements of the first array.

The third line of each test case contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \le b_i \le 100$$$) — elements of the second array.

Output format:
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.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Note:
In the first test case, you can swap the numbers $$$a_3$$$ and $$$b_3$$$, 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 $$$a_1$$$ and $$$b_1$$$, 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 $$$a_7$$$ and $$$b_7$$$, $$$a_8$$$ and $$$b_8$$$, $$$a_9$$$ and $$$b_9$$$, 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.

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

Example output:
Yes
No
Yes
Yes
Yes
No
No

Editorial:
The first solution: Fix the position of the numbers $$$a_n, b_n$$$. And for each other index $$$i$$$, let's check whether the conditions $$$a_i \leq a_n$$$ and $$$b_i \leq b_n$$$ are met. If not, swap $$$a_i$$$ and $$$b_i$$$ and check again. If the conditions are not met for some index in both variants — the answer is "No", otherwise "Yes".
The second solution: Let $$$M$$$ be the maximum of all the numbers $$$a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_n$$$. Then if $$$a_n < M$$$ and $$$b_n < M$$$ the answer is — "No", since in the one of the arrays where the number $$$M$$$ appears after the operations, the maximum will be $$$M$$$, which is greater than $$$a_n$$$ and $$$b_n$$$. Otherwise, either $$$a_n = M$$$ or $$$b_n = M$$$. If $$$a_n = M$$$, then swap $$$a_n$$$ and $$$b_n$$$, now $$$b_n = M$$$. So the condition $$$b_n = \max(b_1, b_2, \ldots, b_n)$$$ will always be met, regardless of the numbers $$$b_1, b_2, \ldots, b_{n-1}$$$. Therefore, it would be best to put in $$$b_i$$$ the maximum of the numbers $$$a_i, b_i$$$ for each $$$i$$$. After that, it remains to check the condition for the array $$$a_1, a_2, \ldots, a_n$$$, and if it is met, the answer is —"Yes", otherwise —"No"