Souvenirs

题意翻译

- 给出 $n$ 以及一个长为 $n$ 的序列 $a$。 - 给出 $m$，接下来 $m$ 组询问。 - 每组询问给出一个 $l,r$，你需要求出，对于 $i,j \in [l,r]$，且满足 $i \neq j$，$|a_i-a_j|$ 的最小值。 - $1 \leq n \leq 10^5$，$1 \leq m \leq 3\times 10^5$，$0 \leq a_i \leq 10^9$。

题目描述

Artsem is on vacation and wants to buy souvenirs for his two teammates. There are $ n $ souvenir shops along the street. In $ i $ -th shop Artsem can buy one souvenir for $ a_{i} $ dollars, and he cannot buy more than one souvenir in one shop. He doesn't want to introduce envy in his team, so he wants to buy two souvenirs with least possible difference in price. Artsem has visited the shopping street $ m $ times. For some strange reason on the $ i $ -th day only shops with numbers from $ l_{i} $ to $ r_{i} $ were operating (weird? yes it is, but have you ever tried to come up with a reasonable legend for a range query problem?). For each visit, Artsem wants to know the minimum possible difference in prices of two different souvenirs he can buy in the opened shops. In other words, for each Artsem's visit you should find the minimum possible value of $ |a_{s}-a_{t}| $ where $ l_{i}<=s,t<=r_{i} $ , $ s≠t $ .

输入输出格式

输入格式

The first line contains an integer $ n $ ( $ 2<=n<=10^{5} $ ). The second line contains $ n $ space-separated integers $ a_{1} $ , ..., $ a_{n} $ ( $ 0<=a_{i}<=10^{9} $ ). The third line contains the number of queries $ m $ ( $ 1<=m<=3·10^{5} $ ). Next $ m $ lines describe the queries. $ i $ -th of these lines contains two space-separated integers $ l_{i} $ and $ r_{i} $ denoting the range of shops working on $ i $ -th day ( $ 1<=l_{i}<r_{i}<=n $ ).

输出格式

Print the answer to each query in a separate line.

输入输出样例

输入样例 #1

8
3 1 4 1 5 9 2 6
4
1 8
1 3
4 8
5 7

输出样例 #1

0
1
1
3