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;

public class ABC_102_C
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        string[] line = Console.ReadLine().Trim().Split(' ');
        
        // Array.ConvertAll<TInput, TOutput>  配列の型をintに変更
        var a = Array.ConvertAll(line, int.Parse);
        var b = new int[n];
        
        // 配列a[i]からiを引いたものを配列bとする
        for (int i = 0; i < n; i++) b[i] = a[i] - (i + 1);
        
        //bを昇順ソート
        Array.Sort(b);
        
        // bの中央値を求める（mdファイル参照）
        var med = b[n / 2];
        Console.WriteLine(getSum(a, med));
    }

        /// <summary>
        /// bを中央値として絶対値の合計を求める
        /// </summary>
        /// <param name="a">元の配列</param>
        /// <param name="b">中央値</param>
        /// <returns></returns>
        public static long getSum(int[] a, int b)
        {
        	// 配列の大きさ
            var n = a.Length;
            // 結果用の変数。long型の0
            var ret = 0L;
            
            // 元の配列に対し、中央値と(i+1)を引いたものを合計していく
            for (int i = 0; i < n; i++)
                ret += Math.Abs(a[i] - b - i - 1);
            return ret;
        }

}