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)

/**
 * @author Finn Lidbetter
 */
import java.util.*;
import java.io.*;
import java.awt.geom.*;

public class Main {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringBuilder sb = new StringBuilder();
    
    int n = Integer.parseInt(br.readLine());
    String[] s = br.readLine().split(" ");
    int[] arr = new int[n];
    for (int i=0; i<n; i++) {
      arr[i] = Integer.parseInt(s[i])-(i+1);
    }
    Arrays.sort(arr);
    int med = arr[n/2];
    long sum = 0;
    for (int i=0; i<n; i++) {
      sum += (long)(Math.abs(arr[i]-med));
    }
    System.out.println(sum);
    /*
    long best = Long.MAX_VALUE;
    while (lo<=hi) {
      int mid = lo + (hi-lo)/2;
      long sum = 0;
      for (int i=0; i<n; i++) {
        sum += (long)(Math.abs(arr[i]-mid));
      }
      if (sum<best) {
        best = sum;
      }
      if ()
    }
    */
  }
}