Maximum Absolute Difference

You are given two integer arrays A and B each of length N. For each test case, your task is to find the maximum absolute difference between any element from A and any element from B. More formally, the answer for a test case is given by:

$$ \max\Big(|\max A - \min B|,\, |\min A - \max B|\Big) $$

The input starts with an integer T specifying the number of test cases. For every test case:

• The first line contains an integer N, which indicates the length of the arrays.
• The second line contains N space-separated integers representing the array A.
• The third line contains N space-separated integers representing the array B.

For each test case, print the maximum absolute difference on a new line.

inputFormat

The first line of the input contains a single integer T – the number of test cases. The description of the test cases follows.

For each test case:

• The first line contains an integer N representing the number of elements in the arrays.
• The second line contains N space-separated integers, the elements of array A.
• The third line contains N space-separated integers, the elements of array B.

outputFormat

For each test case, output a single line containing the maximum absolute difference calculated as:

$$ \max\Big(|\max A - \min B|,\, |\min A - \max B|\Big) $$

## sample

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