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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main
{

  public static void main(String[] args) throws IOException
  {
    BufferedReader r = new BufferedReader(new InputStreamReader(System.in), 1);
    String s = r.readLine();
    int n = Integer.parseInt(s);
    s = r.readLine();
    long a[] = new long[200001];
    String[] sl = s.split("[\\s]+");
    for(int i = 0; i < n; i++)
    {
      a[i] = Long.parseLong(sl[i]);
    }

    for(int i = 0; i < n; i++)
    {
      a[i] -= i + 1;
    }

    //System.out.println(Arrays.toString(a));

    long m = 0;
    for(int i = 0; i < n; i++)
    {
      m += a[i];
    }
    m /= n;

    long min = Long.MAX_VALUE;

    for(int j = -7; j <= 7; j++)
    {
      long t = 0;
      for(int i = 0; i < n; i++)
      {
        t += Math.abs(a[i] - m + j);
      }
      min = Math.min(min, t);
    }

    System.out.println(min);
  }

}