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.util.Arrays;
import java.util.Scanner;

class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int N = scanner.nextInt();
    long sum = 0;
    int[] a = new int[N];
    for (int i = 0; i < N; i++) {
      a[i] = scanner.nextInt() - (i + 1);
      sum += a[i];
    }

    Arrays.sort(a);
    long m1 = compute(a, a[N / 2]);
    if (N == 1) {
      System.out.println(m1);
      return;
    }
    long m2 = compute(a, a[N / 2 + 1]);
    if (m1 < m2) {
      System.out.println(m1);
    } else {
      System.out.println(m2);
    }
  }

  public static long compute(int[] a, long b) {
    long r = 0;
    for (int i = 0; i < a.length; i++) {
      r += Math.abs(a[i] - b);
    }
    return r;
  }
}