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;

namespace AtCoder
{
    class Program
    {
        static int n;
        static List<int> plus = new List<int>();
        static List<int> minus = new List<int>();
        static List<int> veryPlus = new List<int>();
        static List<int> veryMinus = new List<int>();

        static void Main(string[] args)
        {
            //[summary]C - Linear Approximation
            n = int.Parse(Console.ReadLine());
            var a = ReadLine();

            var numbers = GetNumbers(a).ToList();

            int min = numbers.Min();
            int max = numbers.Max();
            int minSadness = int.MaxValue;

            for (int b = min; b <= max; b++)
            {
                int sadness = CalcSadness(b, numbers);

                //Console.WriteLine("{0}/ {1}", b, sadness);

                if (sadness < minSadness)
                {
                    minSadness = sadness;
                }
            }

            Console.WriteLine(minSadness);
        }

        static IEnumerable<int> GetNumbers(List<int> a)
        {
            for(int i = 0; i < n; i++)
            {
                int num = a[i] - (i + 1);

                if (num >= 0)
                {
                    plus.Add(num);
                }
                else
                {
                    minus.Add(num);
                }

                yield return num;
            }
        }

        static int CalcSadness(int b, List<int> numbers)
        {
            int sadness = 0;

            for(int i = 0; i < n; i++)
            {
                sadness += Math.Abs(numbers[i] - b);
            }

            return sadness;
        }

        static List<int> ReadLine()
        {
            var line = Console.ReadLine();
            var array = line.Split(' ');

            return array.Select(x => int.Parse(x)).ToList();
        }
    }
}