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.Linq;

namespace AtCoder
{
    class Program
    {
        static int n;
        static List<long> plus = new List<long>();
        static List<long> minus = new List<long>();
        static List<long> anotherPlus = new List<long>();
        static List<long> anotherMinus = new List<long>();
        static bool isPlus;

        static void Main(string[] args)
        {
            //[summary]C - Linear Approximation
            n = int.Parse(Console.ReadLine());
            var a = ReadLine();

            var numbers = GetNumbers(a).ToList();

            plus = plus.OrderByDescending(x => x).ToList();
            minus = minus.OrderBy(x => x).ToList();

            int min = numbers.Min();
            int max = numbers.Max();
            long minSadness = long.MaxValue;

            for (int b = min; b <= max; b++)
            {
                long sadness = CalcSadness(b);

                //Console.WriteLine("{0}/ {1}", b, sadness);

                if (sadness < minSadness)
                {
                    minSadness = sadness;
                }
            }

            Console.WriteLine(minSadness);
        }
        
        static long CalcSadness(int b)
        {
            long plusSadness = 0;
            long minusSadness = 0;

            if (b < 0)
            {
                while (minus.Count > 0)
                {
                    if (b > minus[0])
                    {
                        anotherMinus.Add(minus[0]);
                        minus.RemoveAt(0);
                    }
                    else
                    {
                        break;
                    }
                }

                minusSadness = Math.Abs(minus.Sum() - b * minus.Count);
                minusSadness += Math.Abs(anotherMinus.Sum() - b * anotherMinus.Count);
                plusSadness += Math.Abs(plus.Sum() - b * plus.Count);
            }
            else
            {
                if (!isPlus)
                {
                    isPlus = true;
                    minus.AddRange(anotherMinus);
                }

                while (plus.Count > 0)
                {
                    if (b > plus[0])
                    {
                        anotherPlus.Add(plus[0]);
                        plus.RemoveAt(0);
                    }
                    else
                    {
                        break;
                    }
                }

                plusSadness = Math.Abs(plus.Sum() - b * plus.Count);
                plusSadness += Math.Abs(anotherPlus.Sum() - b * anotherPlus.Count);
                minusSadness += Math.Abs(minus.Sum() - b * minus.Count);
            } 

            return plusSadness + minusSadness;
        }

        static int CalcSadness(int b, List<int> numbers)
        {
            int sadness = 0;

            for(int i = 0; i < n; i++)
            {
                sadness += Math.Abs(numbers[i] - b);
            }

            return sadness;
        }

        static IEnumerable<int> GetNumbers(List<int> a)
        {
            for (int i = 0; i < n; i++)
            {
                int num = a[i] - (i + 1);

                if (num >= 0)
                {
                    plus.Add(num);
                }
                else
                {
                    minus.Add(num);
                }

                yield return num;
            }
        }

        static List<int> ReadLine()
        {
            var line = Console.ReadLine();
            var array = line.Split(' ');

            return array.Select(x => int.Parse(x)).ToList();
        }
    }
}