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 System.Text;
using static System.Convert;
using static System.Console;
using static System.Math;
class MainClass
{
	static void Main(string[] args)
	{
		Answer();
	}
	public static void Answer()
	{
	　var line = Console.ReadLine().Trim();
      var N = int.Parse(line);
      line = Console.ReadLine().Trim();
      var ArrA = Array.ConvertAll<string, int>(line.Split(' '), new Converter<string, int>(s => int.Parse(s)));
		
      for(var i = 0; i < N; i++)
      {
        ArrA[i] -= (i + 1);
      }
      Array.Sort(ArrA);

      var ArrB = new int[2];
      var exist2patternflg = false;
      if (N % 2 == 0)
      {
        ArrB[0] = ArrA[N / 2 - 1];
        ArrB[1] = ArrA[N / 2];
        exist2patternflg = true;
      }
      else
      {
        ArrB[0] = ArrA[N / 2];
      }

      var sumSad = 0L;
      for(var i = 0; i < N; i++)
      {
        sumSad += Math.Abs(ArrA[i] - ArrB[0]);
      }
      WriteLine(sumSad);
      return;
	}
}