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.*;
 
 
public class Main {
    public static void main(String[] args) {
        // 自分の得意な言語で
        // Let's チャレンジ！！
 
        Scanner sc = new Scanner(System.in);
        int n=Integer.parseInt(sc.nextLine());
        String line = sc.nextLine();
        String s[]=line.split(" ",0);
        int d[]=new int[n];
        for(int i=0;i<n;i++){
            d[i]=Integer.parseInt(s[i])-(i+1);
        }
        
        
        int count=0;
        for(int i=0;i<n-1;i++){
            count=Math.min(count,d[i+1]);
        }count-=n;
        
        int p=0;
        int ans=-1;
        while(ans<p||p==-1){
            p=ans;
            ans=0;
            for(int i=0;i<n;i++){
                ans+=Math.max(d[i]-(count+i+1),-(d[i]-(count+i+1)));
            }
            count++;
        }
        System.out.println(p);
        
    }
}