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.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n + 1];
		int[] data = new int[n + 1];
		for(int i = 1; i <= n; i++) {
			a[i] = sc.nextInt();
			data[i] = a[i] - i;
		}
		quick_sort(1, n, data);
		int b = data[n / 2 + 1];
		int sum = 0;
		for(int i = 1; i <= n; i++) {
			sum += Math.abs(a[i] - (b + i));
		}
		System.out.println(sum);
		
	}
	static void quick_sort(int left, int right, int data[]) {
		if(left >= right) return;
		int pivot = data[left], lower, mid, t;
		for(lower = left, mid = right; lower < mid;) {
			while(lower <= mid && data[lower] <= pivot)
				lower++;
			while(lower <= mid && data[mid] > pivot)
				mid--;
			if(lower < mid) {
				t = data[lower];
				data[lower] = data[mid];
				data[mid] = t;
			}
		}
		t = data[left];
		data[left] = data[mid];
		data[mid] = t;
		quick_sort(left, mid - 1, data);
		quick_sort(mid + 1, right, data);
	}
}