Problem:
Score : 300 points

Problem Statement

Snuke has an integer sequence A of length N.

He will freely choose an integer b.
Here, he will get sad if A_i and b+i are far from each other.
More specifically, the sadness of Snuke is calculated as follows:

abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))

Here, abs(x) is a function that returns the absolute value of x.

Find the minimum possible sadness of Snuke.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible sadness of Snuke.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

2

If we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.
Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
int main() 
{
	int n,i,max=0,j,m=0,ans=0;
	scanf("%d",&n);
	int a[n];
	for(i=1;i<=n;i++)
	{
	    scanf("%d",&a[i]);
	}
	max=a[1];
	for(i=1;i<=n;i++)
	{
	    if(max<a[i])
	    {
	        max=a[i];
	    }
	}
	if(max>=n)
	{
	    ans=max;
	}
	else
	{
	    ans=n;
	}
	int sum[2*(ans)+1],min=0;
	for(i=-ans;i<=ans;i++)
	{
	    sum[m]=0;
	    for(j=1;j<=n;j++)
	    {
	        if((a[j]-j-i)>=0)
	        {
	            sum[m]=sum[m]+a[j]-j-i;
	        }
	        else
	        {
	            sum[m]= sum[m]+i+j-a[j];
	        }
	    }
	    m++;
	}
	min=sum[0];
	for(j=0;j<m;j++)
	{
	    if(min>sum[j])
	    {
	        min=sum[j];
	    }
	}
	printf("%d",min);
	return 0;
}