# 2019 Fall KBTU OPEN

# Students love

Nurdaulet and Zharaskhan are coaching students. To each student they have their own attitudes, it can be expressed as number `a`

(for Nurdaulet) and _{i}`b`

(for Zharaskan) that are called _{i}**love index** of students. Askar asked them to calculate the **unfair attitude rate**. **Unfair attitude rate** is the difference between the largest and the smallest **love index**. In order to not show their possibly large **unfair attitude rates**, they decided to cheat: each shuffle his array, then form new array `c`

= _{i}`a`

+ _{i}`b`

and show the rate of new formed array to Askar. What is the minimal possible rate they can achieve?_{i}

#### Input

On the first line you are given single integer **n** (**1** ≤ **n** ≤ **200000**). On the second line you are given **n** integers `a`

(_{i}`-10`

≤ ^{6}`a`

≤ _{i}`10`

). On the third line you are given ^{6}**n** integers `b`

(_{i}`-10`

≤ ^{6}`b`

≤ _{i}`10`

).^{6}

#### Output

Output single integer, the answer to the problem.

2 -3 -5 3 5

0