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)

// クソ解法
using System;
using System.Linq;
public class Program {
  public static void Main() {
    long N = long.Parse(Console.ReadLine());
    long[] array = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
    for (long i = 0; i < N; i++) {
      array[i] -= i+1;
    }

    long b = (long)Math.Ceiling(array.Sum() / (double)N);
    long past1 = 0, past2 = 0, past3 = 0;
    long[] temp = new long[N];
    while (!(past1 < past2) && !(past2 > past3)) {
      for (long i = 0; i < N; i++) {
        temp[i] = Math.Abs(array[i] - b);
      }
      past3 = past2;
      past2 = past1;
      past1 = temp.Sum();
      b = (past1<past2) ? b+1 : b-1;
    }
    Console.WriteLine(Math.Min(past1, past2));
  }
}