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: Runtime Error)

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

namespace ABC102C_cs
{
    class Program
    {
        static void Main(string[] args)
        {
            int givenN = int.Parse(Console.ReadLine());
            if (givenN == 1)
            {
                Console.WriteLine("0");
                return;
            }
            var givenA = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var changedA = LinearApproximation.ChangedArray(givenA);
            var center = LinearApproximation.Center(givenN);
            var median1 = changedA[center];
            var median2 = changedA[center + 1];
            var result1 = LinearApproximation.Sadness(givenA, median1);
            var result2 = LinearApproximation.Sadness(givenA, median2);
            Console.WriteLine(Math.Min(result1, result2));
        }
    }
    public static class LinearApproximation
    {
        public static int[] ChangedArray(int[] a)
        {
            var result = a.Select((x, i) => x - i - 1).ToArray();
            return result;
        }
        public static int Center(int n)
        {
            return (n - 1) / 2;
        }
        public static int Sadness(int[] a, int b)
        {
            return a.Select((n, i) => Math.Abs(n - (b + i + 1))).Sum();
        }
    }
}