You are given two arrays $$$a$$$ and $$$b$$$ of $$$n$$$ positive integers each. You can apply the following operation to them any number of times:

Select an index $$$i$$$ ($$$1\leq i\leq n$$$) and swap $$$a_i$$$ with $$$b_i$$$ (i. e. $$$a_i$$$ becomes $$$b_i$$$ and vice versa).

Find the minimum possible value of $$$\max(a_1, a_2, \ldots, a_n) \cdot \max(b_1, b_2, \ldots, b_n)$$$ you can get after applying such operation any number of times (possibly zero).

Input

The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 100$$$) — the number of test cases. Description of the test cases follows.

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

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10\,000$$$) where $$$a_i$$$ is the $$$i$$$-th element of the array $$$a$$$.

The third line of each test case contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \le b_i \le 10\,000$$$) where $$$b_i$$$ is the $$$i$$$-th element of the array $$$b$$$.

Output

For each test case, print a single integer, the minimum possible value of $$$\max(a_1, a_2, \ldots, a_n) \cdot \max(b_1, b_2, \ldots, b_n)$$$ you can get after applying such operation any number of times.

Note

In the first test, you can apply the operations at indices $$$2$$$ and $$$6$$$, then $$$a = [1, 4, 6, 5, 1, 5]$$$ and $$$b = [3, 2, 3, 2, 2, 2]$$$, $$$\max(1, 4, 6, 5, 1, 5) \cdot \max(3, 2, 3, 2, 2, 2) = 6 \cdot 3 = 18$$$.

In the second test, no matter how you apply the operations, $$$a = [3, 3, 3]$$$ and $$$b = [3, 3, 3]$$$ will always hold, so the answer is $$$\max(3, 3, 3) \cdot \max(3, 3, 3) = 3 \cdot 3 = 9$$$.

In the third test, you can apply the operation at index $$$1$$$, then $$$a = [2, 2]$$$, $$$b = [1, 1]$$$, so the answer is $$$\max(2, 2) \cdot \max(1, 1) = 2 \cdot 1 = 2$$$.

Min Max Swap

Examples