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;

class Program
{
    #region library
    static int n = 0;
    static int m = 0;
    static int r = 0;
    static int c = 0;
    static int x = 0;
    static int y = 0;
    static int[] arr;
    static string s = "";
    static string[] ss;
    static string alpha = "abcdefghijklmnopqrstuvwxyz";
    static long sum = 0;
    static long cnt = 0;
    static long max = -1;
    static long min = 2147483647;
    static bool flg = false;
    static bool flg2 = false;
    static char[,] map;
    static int[,] imap;
    static string rl()
    {
        return Console.ReadLine();
    }
    static string[] rls()
    {
        return Console.ReadLine().Split();
    }
    static void wl(object obj = null)
    {
        Console.WriteLine(obj);
    }
    static void w(object obj)
    {
        Console.Write(obj);
    }
    static int Int(string s)
    {
        return int.Parse(s);
    }
    static void yes()
    {
        wl("YES");
    }
    static void no()
    {
        wl("NO");
    }
    static void Sum()
    {
        wl(sum);
    }
    static void Cnt()
    {
        wl(cnt);
    }
    static void setarray(int num = -1)
    {
        arr = new int[n];
        if(num == -1) ss = rls();
        for (int i = 0; i < n; i++)
        {
            if (num == -1)
                arr[i] = Int(ss[i]);
            else
                arr[i] = num;
        }
    }
    static void setmap(char def = '@')
    {
        if (r == 0 && c == 0)
        {
            ss = rls();
            r = Int(ss[0]);
            c = Int(ss[1]);
        }
        map = new char[r, c];
        for (int i = 0; i < r; i++)
        {
            if (def == '@') s = rl();
            for (int j = 0; j < c; j++)
            {
                map[i, j] = (def == '@') ? s[j] : def;
            }
        }
    }
    static void setimap(int def = -1)
    {
        if (r == 0 && c == 0)
        {
            ss = rls();
            r = Int(ss[0]);
            c = Int(ss[1]);
        }
        imap = new int[r, c];
        for (int i = 0; i < r; i++)
        {
            if (def == -1) s = rl();
            for (int j = 0; j < c; j++)
            {
                imap[i, j] = (def == -1) ? Int(s[j].ToString()) : def;
            }
        }
    }
    #endregion

    static void Main(string[] args)
    {
        n = Int(rl());
        ss = rls();
        arr = new int[n];
        for (int i = 0; i < n; i++)
        {
            arr[i] = Int(ss[i]) - (i + 1);
        }

        Array.Sort(arr);

        int b = arr[arr.Length / 2];

        for (int i = 0; i < n; i++)
        {
            sum += Math.Abs(Int(ss[i]) - (b + i + 1));
        }
        min = sum;

        if (arr.Length % 2 == 0)
        {
            b = arr[arr.Length / 2 - 1];
            sum = 0;
            for (int i = 0; i < n; i++)
            {
                sum += Math.Abs(Int(ss[i]) - (b + i + 1));
            }
            min = Math.Min(min, sum);
        }

        wl(min);
    }


}