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;

namespace AtCoder.ABC._102
{
    class c
    {
        static void Main(string[] args)
        {
            var line = Console.ReadLine().Trim();
            var N = int.Parse(line);
            line = Console.ReadLine().Trim();
            var A = Array.ConvertAll<string, int>(line.Split(' '), new Converter<string, int>(s => int.Parse(s)));
            for(var i = 0; i < N; ++i)
            {
                A[i] -= i + 1;
            }
            Array.Sort(A);
            var b = new int[2];
            var flg = false;
            if (N % 2 == 0)
            {
                b[0] = A[N / 2 - 1];
                b[1] = A[N / 2];
                flg = true;
            }
            else
            {
                b[0] = A[N / 2];
            }
            var sum = 0L;
            for(var i = 0; i < N; ++i)
            {
                sum += Math.Abs(A[i] - b[0]);
            }
            if(flg && b[0] != b[1])
            {
                var sum2 = 0L;
                for (var i = 0; i < N; ++i)
                {
                    sum2 += Math.Abs(A[i] - b[0]);
                }
                if (sum2 < sum) sum = sum2;
            }
            Console.WriteLine(sum);
        }
    }
}