Perform Easily

题意翻译

给定数组a(长度为6)然后给定长度为n的数组b，然后把$b_i$-$a_{1-6}$中任意一个，使得处理后的b数组跨度（最大值减最小值）最小 $ 1 \leq n \leq 100\,000$ $ 1 \leq a_{i} \leq 10^{9}$ $ 1 \leq b_{i} \leq 10^{9}$

题目描述

After battling Shikamaru, Tayuya decided that her flute is too predictable, and replaced it with a guitar. The guitar has $ 6 $ strings and an infinite number of frets numbered from $ 1 $ . Fretting the fret number $ j $ on the $ i $ -th string produces the note $ a_{i} + j $ . Tayuya wants to play a melody of $ n $ notes. Each note can be played on different string-fret combination. The easiness of performance depends on the difference between the maximal and the minimal indices of used frets. The less this difference is, the easier it is to perform the technique. Please determine the minimal possible difference. For example, if $ a = [1, 1, 2, 2, 3, 3] $ , and the sequence of notes is $ 4, 11, 11, 12, 12, 13, 13 $ (corresponding to the second example), we can play the first note on the first string, and all the other notes on the sixth string. Then the maximal fret will be $ 10 $ , the minimal one will be $ 3 $ , and the answer is $ 10 - 3 = 7 $ , as shown on the picture. 

输入输出格式

输入格式

The first line contains $ 6 $ space-separated numbers $ a_{1} $ , $ a_{2} $ , ..., $ a_{6} $ ( $ 1 \leq a_{i} \leq 10^{9} $ ) which describe the Tayuya's strings. The second line contains the only integer $ n $ ( $ 1 \leq n \leq 100\,000 $ ) standing for the number of notes in the melody. The third line consists of $ n $ integers $ b_{1} $ , $ b_{2} $ , ..., $ b_{n} $ ( $ 1 \leq b_{i} \leq 10^{9} $ ), separated by space. They describe the notes to be played. It's guaranteed that $ b_i > a_j $ for all $ 1\leq i\leq n $ and $ 1\leq j\leq 6 $ , in other words, you can play each note on any string.

输出格式

Print the minimal possible difference of the maximal and the minimal indices of used frets.

输入输出样例

输入样例 #1

1 4 100 10 30 5
6
101 104 105 110 130 200

输出样例 #1

0

输入样例 #2

1 1 2 2 3 3
7
13 4 11 12 11 13 12

输出样例 #2

7

说明

In the first sample test it is optimal to play the first note on the first string, the second note on the second string, the third note on the sixth string, the fourth note on the fourth string, the fifth note on the fifth string, and the sixth note on the third string. In this case the $ 100 $ -th fret is used each time, so the difference is $ 100 - 100 = 0 $ . In the second test it's optimal, for example, to play the second note on the first string, and all the other notes on the sixth string. Then the maximal fret will be $ 10 $ , the minimal one will be $ 3 $ , and the answer is $ 10 - 3 = 7 $ .