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

namespace AtCoder
{
	public class ABC
	{
		static readonly int mod = 1000000007;  // 10^9+7

		static void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });


			//string s = Console.ReadLine();
			int n = int.Parse(Console.ReadLine());
			//long x = long.Parse(Console.ReadLine());
			int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
			//long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();
			int sum = 0;
			for (int i = 0; i < n; i++) {
				sum += a[i] - (i + 1);
			}
			int avr = sum / n;
			long[] ans = new long[3];
			for (int i = 0; i < n; i++) {
				ans[0] += Math.Abs(a[i] - (avr + i));
				ans[1] += Math.Abs(a[i] - (avr + i + 1));
				ans[2] += Math.Abs(a[i] - (avr + i + 2));
			}
			Console.WriteLine(Math.Min(ans[0], Math.Min(ans[1], ans[2])));


			Console.Out.Flush();
		}
	}
}