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.Generic;
using System.Linq;

namespace ConsoleApp1
{
	class Program
	{
		static void Main(string[] args)
		{
			var length = long.Parse(Console.ReadLine());
			var inputs = Console.ReadLine().Split(' ').Select(text => long.Parse(text)).ToList();

			var counts = new Dictionary<long, int>();
			for (int i = 0; i < length; i++)
			{
				var difference = inputs[i] - (i + 1);
				if (!counts.ContainsKey(difference))
				{
					counts.Add(difference, 0);
				}
				counts[difference]++;
			}

			KeyValuePair<long, int> maxPair = new KeyValuePair<long, int>(0, 0);
			var bs = new List<long>();
			foreach(var pair in counts)
			{
				if (maxPair.Value < pair.Value)
				{
					maxPair = pair;
					bs = new List<long> { pair.Key };
				}
				if (maxPair.Value == pair.Value)
				{
					bs.Add(pair.Key);
				}
			}

			var sortedBs = bs.OrderBy(item => item).ToList();

			var index = sortedBs.Count / 2;

			Console.WriteLine(s(inputs, bs[index], length));
		}

		private static long s(List<long> inputs, long b, long length)
		{
			long max = 0;
			for (int i = 0; i < length; i++)
			{
				max += Math.Abs(inputs[i] - b - (i + 1));
			}
			return max;
		}
	}
}