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.Linq;

namespace ARC100_A
{
    internal class Program
    {
        public static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            long[] a = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);

            long[] temp = a;
            for (int i = 0; i < n; i++)
            {
                temp[i] -= i;
            }

            Array.Sort(temp);
            temp = temp.Select(c => c - temp[0]).ToArray();

            long cur = temp[0];
            long[] asc = new long[n+1];
            asc[0] = 0;
            for (int i = 1; i < n; i++)
            {
                if (temp[i] != cur)
                {
                    cur = temp[i];
                    asc[i] = Math.Abs(cur - temp[i - 1]) * (i) + asc[i - 1];
                    continue;
                }

                asc[i] = asc[i - 1];
            }

            asc[n] = asc[n - 1];

            cur = temp[n - 1];
            long[] desc = new long[n+1];
            for (int i = n - 1; i > 0; i--)
            {
                if (temp[i] != cur)
                {
                    cur = temp[i];
                    desc[i] = Math.Abs(cur - temp[i + 1]) * (n - i - 1) + desc[i + 1];
                    continue;
                }

                desc[i] = desc[i + 1];
            }
            desc[0] = desc[1];

            long min = Int64.MaxValue;
            for (int i = 0; i <= n; i++)
            {
                min = Math.Min(min, asc[i] + desc[i]);
            }
            
            Console.WriteLine(min);
        }
    }
}