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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC_C
{
    class C102
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            List<long> A = Console.ReadLine().Split(' ')
                .Select((x, i) => long.Parse(x) - i).ToList();
            A.Sort();
            //double aved = A.Average();
            //int ave = (int)Math.Round(aved);
            //int abs = A.Sum(x => Math.Abs(x - ave));
            //Console.WriteLine(abs);

            long sumR = 0, sumL = 0, minSum = 0;
            long b = A[0];
            foreach (int a in A)
            {
                sumR += a - b;
            }
            minSum = sumR;

            for(int i = 1; i < N; i++)
            {
                long d = A[i] - A[i - 1];
                sumR -= (N - i) * d;
                sumL += i * d;
                long sum = sumL + sumR;
                if (sum < minSum) minSum = sum;
            }

            Console.WriteLine(minSum);
        }

    }
}