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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static MyUtil;

class MyUtil
{
    public static long[] ReadLongArray()
    {
	return ReadLine().Split().Select(x => long.Parse(x)).ToArray();
    }

    public static long Median(long[] x) 
    {
	int ct = x.Count();
	var y = new long[ct];
	Array.Copy(x, y, ct);
	Array.Sort(y);
	
	if (ct % 2 == 1)
	{
	    return y[ct / 2];
	}
	else
	{
	    var y1 = y[ct/2 - 1];
	    var y2 = y[ct/2];
	    return (y1 + y2) / 2;
	}
    }
}

class Program
{
    public static void Main()
    {
	int n = int.Parse(ReadLine());
	var a = ReadLongArray();

	// b_i = a_i -i and it will calculate the average of b_is, ave
	var b = new long[n];
	for (int i = 0; i < n; i++)
	{
	    b[i] = a[i] - (i+1); // caution a[i] = A_(i+1)
	}
	
	long ave = (long) Median(b);

	long sudness = 0;
	for (int i = 0; i < n; i++)
	{
	    sudness += Math.Abs(a[i] - (ave+i+1));
	}
	WriteLine(sudness);
    }
}