Migrated from Lutece 929 Post office

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Description

There are $N(N \leq 1000)$ villages along a straight road, numbered from $1$ to $N$ for simplicity. We know exactly the position of every one (noted pos$[i]$,pos$[i]$ is positive integer and pos$[i] \leq 10^8$). The local authority wants to build a post office for the people living in the range $i$ to j(inclusive). He wants to make the sum of |pos$[k]-$position_of_postoffice| $(i \leq k \leq j)$ is minimum.

Input

For each test case, the first line is $n$. Then $n$ integer, representing the position of every village and in ascending order. Then a integer $q (q \leq 200000)$, representing the queries. Following $q$ lines, every line consists of two integers $i$ and $j$. the input file is end with EOF. Total number of test case is no more than $10$.

Be careful, the position of two villages may be the same.

Output

For every query of each test case, you tell the minimum sum.

Samples

3
1 2 3
2
1 3
2 3

2
1

Note

Huge input,scanf is recommend.

Resources

2011 Heilongjiang collegiate programming contest