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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(br.readLine());
		String[] aline = br.readLine().split(" ");

		ArrayList<Integer> alist = new ArrayList<Integer>(n);
		ArrayList<Integer> difflist = new ArrayList<Integer>(n);

		for (int i = 0; i < n; i++) {
			int a = Integer.parseInt(aline[i]);
			alist.add(a);
			difflist.add(a - (i + 1));
		}

		Collections.sort(difflist);

		if (n % 2 == 1) {
			int d = difflist.get(n / 2);
			int minsad = 0;
			for (int i = 0; i < n; i++) {
				minsad += Math.abs(alist.get(i) - (d + i + 1));
			}
			System.out.println(minsad);
		} else {
			int d1 = difflist.get(n / 2);
			int d2 = difflist.get(n / 2 - 1);
			int minsad1 = 0;
			int minsad2 = 0;
			for (int i = 0; i < n; i++) {
				minsad1 += Math.abs(alist.get(i) - (d1 + i + 1));
				minsad2 += Math.abs(alist.get(i) - (d2 + i + 1));
			}
			System.out.println(Math.min(minsad1, minsad2));
		}

	}

}