Minimum Difficulty

题意翻译

题目描述 给你n个数，让你去掉其中的一个数，首尾两个数不能去掉，需要你求最小差异。差异是这样定义的：去掉后的数字中，每相邻两个数会产生一个差异值，所有差异值中的最大值，就为这些数字的差异。需要你选择去掉一个数字，使得差异最小，输出最小差异。 输入 输入n，然后第二行输入n个整数ai 输出 输出最小差异 样例输入 5 1 2 3 4 5 样例输出 2 输入： 3 1 4 6 输出： 5 输入： 5 1 2 3 7 8 输出： 4 【数据规模和约定】 3<=n<=100, 1<=ai<=1000

题目描述

Mike is trying rock climbing but he is awful at it. There are $ n $ holds on the wall, $ i $ -th hold is at height $ a_{i} $ off the ground. Besides, let the sequence $ a_{i} $ increase, that is, $ a_{i}<a_{i+1} $ for all $ i $ from 1 to $ n-1 $ ; we will call such sequence a track. Mike thinks that the track $ a_{1} $ , ..., $ a_{n} $ has difficulty . In other words, difficulty equals the maximum distance between two holds that are adjacent in height. Today Mike decided to cover the track with holds hanging on heights $ a_{1} $ , ..., $ a_{n} $ . To make the problem harder, Mike decided to remove one hold, that is, remove one element of the sequence (for example, if we take the sequence $ (1,2,3,4,5) $ and remove the third element from it, we obtain the sequence $ (1,2,4,5) $ ). However, as Mike is awful at climbing, he wants the final difficulty (i.e. the maximum difference of heights between adjacent holds after removing the hold) to be as small as possible among all possible options of removing a hold. The first and last holds must stay at their positions. Help Mike determine the minimum difficulty of the track after removing one hold.

输入输出格式

输入格式

Mike is trying rock climbing but he is awful at it. There are $ n $ holds on the wall, $ i $ -th hold is at height $ a_{i} $ off the ground. Besides, let the sequence $ a_{i} $ increase, that is, $ a_{i}<a_{i+1} $ for all $ i $ from 1 to $ n-1 $ ; we will call such sequence a track. Mike thinks that the track $ a_{1} $ , ..., $ a_{n} $ has difficulty . In other words, difficulty equals the maximum distance between two holds that are adjacent in height. Today Mike decided to cover the track with holds hanging on heights $ a_{1} $ , ..., $ a_{n} $ . To make the problem harder, Mike decided to remove one hold, that is, remove one element of the sequence (for example, if we take the sequence $ (1,2,3,4,5) $ and remove the third element from it, we obtain the sequence $ (1,2,4,5) $ ). However, as Mike is awful at climbing, he wants the final difficulty (i.e. the maximum difference of heights between adjacent holds after removing the hold) to be as small as possible among all possible options of removing a hold. The first and last holds must stay at their positions. Help Mike determine the minimum difficulty of the track after removing one hold.

输出格式

Print a single number — the minimum difficulty of the track after removing a single hold.

输入输出样例

输入样例 #1

3
1 4 6

输出样例 #1

5

输入样例 #2

5
1 2 3 4 5

输出样例 #2

2

输入样例 #3

5
1 2 3 7 8

输出样例 #3

4

说明

In the first sample you can remove only the second hold, then the sequence looks like $ (1,6) $ , the maximum difference of the neighboring elements equals 5. In the second test after removing every hold the difficulty equals 2. In the third test you can obtain sequences $ (1,3,7,8) $ , $ (1,2,7,8) $ , $ (1,2,3,8) $ , for which the difficulty is 4, 5 and 5, respectively. Thus, after removing the second element we obtain the optimal answer — 4.