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 a1, a2, ..., an (1 ≤ ai ≤ 109) - the numbers in Alice’s array.

The third line contains n integers b1, b2, ..., bn (1 ≤ bi ≤ 109) - the numbers in Bob’s array.

Output

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

Explanation

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.