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.*;
import java.util.*;

public class Main {
	private static final int READ_COUNT = 2;
	private static List<String> strList = new ArrayList<>();
	
	public static void main(String[] args) {
		read();
		
		int n = Integer.parseInt(strList.get(0));
		int[] as = new int[n];
		int tmpI = 0;
		for (String str : strList.get(1).split(" ")) {
			as[tmpI] = Integer.parseInt(str) - (tmpI + 1);
			tmpI++;
		}
		
		int minSunuke = 0;
		for (int i = 0; i < n; i++) {
			minSunuke += Math.abs(as[i]);
		}
		
		for (int i = 1; ; i++) {
			int sunuke = 0;
			
			for (int j = 0; j < n; j++) {
				sunuke += Math.abs(as[j] - i);
			}
			
			if (sunuke > minSunuke) {
				break;
			}
			
			minSunuke = sunuke;
		}
		
		for (int i = -1; ; i--) {
			int sunuke = 0;
			
			for (int j = 0; j < n; j++) {
				sunuke += Math.abs(as[j] - i);
			}
			
			if (sunuke > minSunuke) {
				break;
			}
			
			minSunuke = sunuke;
		}
		
		System.out.println(minSunuke);
	}
	
	private static void read() {
		try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {
			for (int i = 0; i < READ_COUNT; i++) {
				strList.add(br.readLine());
			}
		} catch (IOException e) {
		}
	}
}