Absolute Game

Alice and Bob are playing a game. Alice has an array a of n integers, Bob has an array b of n integers. In each turn, a player removes one element of his array. Players take turns alternately. Alice goes first.

The game ends when both arrays contain exactly one element. Let x be the last element in Alice’s array and y be the last element in Bob’s array. Alice wants to maximize the absolute difference between x and y while Bob wants to minimize this value. Both players are playing optimally.Find what will be the final value of the game.

Input

The first line contains a single integer n (1 ≤ n ≤ 1000) - the number of values in each array.

The second line contains n integers a[1], a[2], ..., a[n] (1 ≤ a[i] ≤ 10^9) - the numbers in Alice’s array.

The third line contains n integers b[1], b[2], ..., b[n] (1 ≤ b[i] ≤ 10^9) - the numbers in Bob’s array.

Output

Print the absolute difference between x and y if both players are playing optimally.

Examples

Note

In the first example, the x = 14 and y = 10. Therefore, the difference between these two values is 4.

In the second example, the size of the arrays is already 1. Therefore, x = 14 and y = 42.