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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics; 

class _Class
{
  void _Do()
  {
    var N = Split.ints()[0];
    var Ai = Split.ints();

    for(int i=0;i<N ;i++ )
    {
      Ai[i] -= i;
    }

    long tmp = 0;
    for (int i = 0; i < N; i++)
    {
      tmp += Ai[i];
    }
    tmp /= N;

    long min = long.MaxValue;
    long a = 0;
    for (int i = 0; i < N; i++)
        a +=Math.Abs(Ai[i] - tmp - 1);
    min = Math.Min(min,a);

    a = 0;
    for (int i = 0; i < N; i++)
      a += Math.Abs(Ai[i] - tmp );
    min = Math.Min(min, a);

    a = 0;
    for (int i = 0; i < N; i++)
      a += Math.Abs(Ai[i] - tmp + 1);
    min = Math.Min(min, a);
    Console.WriteLine(min);

  }


  //
  static void Main(string[] args)
  {
    _(args);
    new _Class()._Do();
  }

  [Conditional("DEBUG")]
  static void _(string[] args)
  {
    if (args.Length != 0 && File.Exists(args[0]))
      Console.SetIn(new StreamReader(args[0]));
    else
      Console.Error.WriteLine("in");
  }
}

static class Split
{


  // 1
  public static string[] strings()
  {
    return Console.ReadLine().Split();
  }


  // [2.1] -2,147,483,648 ~ +2,147,483,647
  public static int[] ints()
  {
    var _s = Console.ReadLine().Split();

    var x = new int[_s.Length];
    for (var i = 0; i < _s.Length; i++)
      x[i] = int.Parse(_s[i]);

    return x;
  }

  // [2.2] 
  // -9,223,372,036,854,775,808 ~ 
  // +9,223,372,036,854,775,807
  public static long[] longs()
  {
    var _s = Console.ReadLine().Split();

    var x = new long[_s.Length];
    for (var i = 0; i < _s.Length; i++)
      x[i] = long.Parse(_s[i]);

    return x;
  }

  public static double[] doubles()
  {
    var _s = Console.ReadLine().Split();

    var x = new double[_s.Length];
    for (var i = 0; i < _s.Length; i++)
      x[i] = double.Parse(_s[i]);

    return x;
  }

  public static BigInteger[] bigs()
  {
    var _s = Console.ReadLine().Split();

    var x = new BigInteger[_s.Length];
    for (var i = 0; i < _s.Length; i++)
      x[i] = BigInteger.Parse(_s[i]);

    return x;
  }
}