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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Contest.cs
{
	class Program
	{
		static void Main(string[] args)
		{
			ReadInt();
			var input = ReadInt();
			ulong ans = ulong.MaxValue;
			for(int i = 0; i < input.Length; i++)
			{
				input[i] = input[i] - (i + 1);
			}
			int lower = input.Min();
			if (input.Average() > 0 && input.Min() < 0)
			{
				lower = 0;
			}
			int upper = input.Max();
			if(input.Average() <= 0 && input.Max() > 0)
			{
				upper = 0;
			}
			int b2;
			for(int b = lower;b <= upper; b++)
			{
				ulong sum = 0;
				for(int i = 0;i < input.Length; i++)
				{
					sum += (ulong)Math.Abs(input[i] - b);
					if(sum >= ans)
					{
						break;
					}
				}
				if(sum < ans)
				{
					ans = sum;
					b2 = b;
				}
			}
			Console.WriteLine(ans);
		}

		static string[] ReadStr()
		{
			return Console.ReadLine().Split(' ').ToArray();

		}

		static int[] ReadInt()
		{
			return Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
		}
	}
}