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.Linq;
using System.Collections.Generic;

class Cmondai
{
    static void Main()
    {
        var N = Int64.Parse(Console.ReadLine());
        var A = Console.ReadLine().Split(' ').Select(x => Int64.Parse(x)).ToArray();
        var array = new long[N];
        for (long i=0;i<N;++i)
        {
            array[i]= A[i] - (i + 1);
        }
        array=array.OrderBy(x => x).ToArray();
        var num = (N + 1) / 2;
        var ans = 0L;
        if (N % 2 == 0)
        {
            num = (array[num - 1] + array[num]) / 2;
            ans=Math.Min(GetAns(N,A,num-1),
                Math.Min(GetAns(N,A,num),GetAns(N,A,num+1)));
        }
        else
        {
            num = array[num - 1];
            ans = GetAns(N, A, num);
        }
        Console.WriteLine(ans);
    }
    static long GetAns(long N,long[] A,long num)
    {
        var ans = 0L;
        for (long i = 0; i < N; ++i)
        {
            ans += Math.Abs(A[i] - (i + 1 + num));
        }
        return ans;
    }
}