Assign Mice to Holes

There are N Mice and N holes that are placed in a straight line. Each hole can accomodate only 1 mouse.

The positions of Mice are denoted by array A and the position of holes are denoted by array B.

A mouse can stay at his position, move one step right from x to x + 1, or move one step left from x to x − 1. Any of these moves consumes 1 minute.

Assign mice to holes so that the time when the last mouse gets inside a hole is minimized.

1 <= N <= 10⁵

-10⁹ <= A[i], B[i] <= 10⁹

First argument is an integer array A.

Second argument is an integer array B.

Return an integer denoting the minimum time when the last nouse gets inside the holes.

Input 1:

 A = [-4, 2, 3]
 B = [0, -2, 4]

Input 2:

 A = [-2]
 B = [-6]

Output 1:

 2

Output 2:

 4

Explanation 1:

 Assign the mouse at position (-4 to -2), (2 to 0) and (3 to 4).
 The number of moves required will be 2, 2 and 1 respectively.
 So, the time taken will be 2.

Explanation 2:

 Assign the mouse at position -2 to -6.
 The number of moves required will be 4.
 So, the time taken will be 4.