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

namespace Contest
{
    class Scanner
    {
        private string[] line = new string[0];
        private int index = 0;

        public string Next()
        {
            if (line.Length <= index)
            {
                line = Console.ReadLine().Split(' ');
                index = 0;
            }

            var res = line[index];
            index++;
            return res;
        }

        public int NextInt()
        {
            return int.Parse(Next());
        }

        public long NextLong()
        {
            return long.Parse(Next());
        }

        public string[] Array()
        {
            line = Console.ReadLine().Split(' ');
            index = line.Length;
            return line;
        }

        public int[] IntArray(int n)
        {
            var array = Array();
            var result = new int[n];
            for (int i = 0; i < n; i++)
            {
                result[i] = int.Parse(array[i]);
            }

            return result;
        }

        public int[] IntArray()
        {
            var array = Array();
            var result = new int[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = int.Parse(array[i]);
            }

            return result;
        }


        public long[] LongArray()
        {
            var array = Array();
            var result = new long[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = long.Parse(array[i]);
            }

            return result;
        }

        public uint NextUint()
        {
            return uint.Parse(Next());
        }
    }

    class Program
    {
        private int N;
        private int[] A;
        private void Scan()
        {
            var sc = new Scanner();
            N = sc.NextInt();
            A = sc.IntArray();
        }


        public void Solve()
        {
            Scan();
            Console.WriteLine(Calc(Min(-1000000000, 1000000000)));
        }

        private int Min(int from, int to)
        {
            while (to - from > 1)
            {
                int mid = (from + to) / 2;
                if (Calc(mid) - Calc(mid - 1) < 0)
                {
                    from = mid;
                }
                else
                {
                    to = mid;
                }
            }

            return from;
        }

        private long Calc(int b)
        {
            long result = 0;
            for (int i = 0; i < N; i++)
            {
                result += Math.Abs(A[i] - (b + i + 1));
            }

            return result;
        }


        static void Main() => new Program().Solve();
    }
}