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.Threading.Tasks;



class Program
{
    const int MOD = 1000000007;
    const int INF = 1 << 30;

    static void Main(string[] args)
    {
        Solve();
    }




    static void Solve()
    {
        Scan sc = new Scan();
        write wr = new write();

        int[] s = sc.intarr;
        long N = s[0];
        var A = sc.longarr;
        for(int i = 0; i < N; ++i)
        {
            A[i] -= i+1;
        }

        Array.Sort(A);
        long b1 = A[N / 2];

        long ans1 = 0;
        for(int i = 0; i < N; ++i)
        {
            ans1 += Math.Abs(A[i] - b1);
        }
        wr.wri(ans1);
    }
}
    




class Scan
{
        public string str => Console.ReadLine();

        public string[] strarr => str.Split(' ');

        public long[] longarr => strarr.Select(long.Parse).ToArray();
        public int[] intarr => strarr.Select(int.Parse).ToArray();
    public char[] chararr => str.ToArray();


}



class write
{
    public void wri<Type>(Type x)
    {
        Console.WriteLine(x);
    }
}