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: Time Limit Exceeded)

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