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: Accepted)

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

public class Main {

  public static void main(String[] args) {

    new Main().run();
  }
  public void run() {
    
    try(BufferedReader in = new BufferedReader(new InputStreamReader(System.in))) {

      int n = Integer.parseInt(in.readLine());
      String line = in.readLine();
      int[] ax = new int[n];
      long sum = 0;

      int m;
      int offset=0,next=0;
      char regex = ' ';
      boolean isContinue = true;
      for(int i=0; isContinue; i++) {
        if((next = line.indexOf(regex,offset)) == -1) {
          next = line.length();
          isContinue = false;
        }
        m = Integer.parseInt(line.substring(offset,next));
        m -= i;
        ax[i] = --m;
        offset = ++next;
      }

      Arrays.parallelSort(ax);
      int b = ax[n/2];

      for (int i : ax) {
        sum += Math.abs(i-b);
      }

      System.out.println(sum);

    }
    catch(IOException e) {
      System.err.println(e);
    }
  }
}