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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
//var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
namespace AtCoderSolve
{
    class Solve
    {
        const int mod = 1000000007;
        static void Main(string[] args)
        {
            //var watch = new Stopwatch();
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            int N = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(int.Parse).ToArray();
            for(var i = 0; i < N; i++)
            {
                a[i] -= i + 1;
            }
            if (N == 1)
            {
                Console.WriteLine(a[0]);
                Console.Out.Flush();
                return;
            }
            int m = N % 2 != 0 ? a[N / 2] : (a[N / 2] + a[N / 2 - 1]) / 2;

            long ans = 0;
            for(var i = 0; i < N; i++)
            {
                ans += Math.Abs(a[i] - m);
            }
            if (N % 2 == 0)
            {
                long sum = 0;
                for(var i = 0; i < N; i++)
                {
                    sum += Math.Abs(a[i] - m - 1);
                }
                ans = Math.Min(ans, sum);
            }

            Console.WriteLine(ans);
            
            //watch.Start();

           

            Console.Out.Flush();
            /*watch.Stop();

            Console.WriteLine($"time:{watch.ElapsedMilliseconds} ms"); //Debug Only.
            Console.Out.Flush();*/
        }
    }
    


    public class Calculation
    {
        
    }

    public class Graph
    {

    }
}