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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace ABC
{
    class ProgramC
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split(" ").Select(x => int.Parse(x)).ToList();
            var result = long.MaxValue;

            var b = new List<int>();
            for (var i = 0; i < n; i++)
            {
                b.Add(a[i] - (i + 1));
            }

            b.Sort();

            if (n % 2 == 0)
            {
                var b1 = n / 2;
                var b2 = b1 + 1;
                for (var i = b1; i <= b2; i++)
                {
                    result = Math.Min(result, calc(a, b[i]));
                }
            }
            else
            {
                result = calc(a, b[n / 2]);
            }

            Console.WriteLine(result);
        }

        static long calc(List<int> list, int b)
        {
            var result = 0L;
            for (var i = 0; i < list.Count; i++)
            {
                result += Math.Abs(list[i] - (b + i + 1));
            }
            return result;
        }
    }
}