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;

class Linear{
    static void Main(string[] args){
        var n = int.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split(' ');
        var aArray = new int[n];
        var sum = 0;
        var nSum = 0;
        for(int i=0; i<n; i++){
            aArray[i] = int.Parse(a[i]);
            sum += aArray[i];
            nSum += i + 1;
        }

        var b = (sum/n) - nSum/n;
        Console.WriteLine("b : {0}", b);
        var result1 = getSad(aArray, b);
        var result2 = getSad(aArray, b-1);
        var result3 = getSad(aArray, b+1);

        var result = Math.Min(result3, Math.Min(result1, result2));
        Console.WriteLine(result);
    }

    static int getSad(int[] aArray, int b){
        var result = 0;
        for(int i=0; i<aArray.Length; i++){
            result += Math.Abs(aArray[i] - (b+i));
        }
        return result;
    }
}