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.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const long Mod = 1000000007;

    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static object process(TextReader input) {
        var n = int.Parse(input.ReadLine());
        var aa = ToIntArray(input.ReadLine(), n);

        Func<long, long> f = (x) => {
            return aa.Sum(a => Math.Abs(a - x));
        };

        for (int i=0; i<n; i++) {
            aa[i] -= (i + 1);
        }

        var ave = (long)aa.Average();

        var min = long.MaxValue;
        var minb = 0L;

        var fb = 0L;
        var b = 0L;

        b = ave + 0; fb = f(b); if (fb < min) { min = fb; minb = b; }
        b = ave + 1; fb = f(b); if (fb < min) { min = fb; minb = b; }
        b = ave - 1; fb = f(b); if (fb < min) { min = fb; minb = b; }
        b = -ave + 0; fb = f(b); if (fb < min) { min = fb; minb = b; }
        b = -ave + 1; fb = f(b); if (fb < min) { min = fb; minb = b; }
        b = -ave - 1; fb = f(b); if (fb < min) { min = fb; minb = b; }

        Debug.WriteLine(minb);

        return min;
    }

    static long[] ToIntArray(string strs, int n) {
        var ret = new long[n];
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = long.Parse(spl[i]);
        return ret;
    }
}