Students love#9410
Nurdaulet and Zharaskhan are coaching students. To each student they have their own attitudes, it can be expressed as number a_i (for Nurdaulet) and b_i (for Zharaskan) that are called **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_i and show the rate of new formed array to Askar. What is the minimal possible rate they can achieve?
On the first line you are given single integer (1 \leq n \leq 200000). On the second line you are given integers a_i (-10^6 \leq a_i \leq 10^6). On the third line you are given integers b_i (-10^6 \leq b_i \leq 10^6).
Output single integer, the answer to the problem.
Example 1