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.awt.Point;
import java.util.ArrayDeque;
import java.util.Scanner;
import java.util.*;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Set;
import java.util.HashSet;
import java.util.Collection;


 
public class Main{
	
        static final Scanner sc=new Scanner(System.in);
        
        
        
        
        
        
        public static void main(String[]args){
                int N=sc.nextInt();
                int[]A=new int[N];
                for(int i=0;i<N;i++){
                        A[i]=sc.nextInt();
                }
                int[]B=new int[N];
                for(int i=1;i<N+1;i++){
                        B[i-1]=A[i-1]-i;
                }
                Arrays.sort(B);
                int x=B[N/2];
                int y=B[N/2];
                int minx=100;
                int miny=100;
                
                while(true){
                        int sum=0;
                        for(int i=0;i<N;i++){
                                sum+=Math.abs(B[i]-x);


                        }
                        if(sum<minx){
                                minx=sum;
                                
                        }
                        if(x<B[(99/100)*N]){
                                x++;
                        }else{
                                break;
                        }

                        
                }
                while(true){
                        int sum=0;
                        for(int i=0;i<N;i++){
                                sum+=Math.abs(B[i]-y);


                        }
                        if(sum<miny){
                                miny=sum;
                        }
                        if(y>B[(99/100)*N]){
                                y--;
                        }else{
                                break;
                        }
                        
                }
                System.out.println(Math.min(minx,miny));
                
        }
        
        
        

		
	
}