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.*;

class Main{
    public static void main(String[] args){
        solve();
    }

    public static void solve(){
        Scanner sc = new Scanner(System.in);
     	int n = sc.nextInt();
     	int[] a = new int[n];
     	int b = 0;
     	for(int i=0;i<n;i++){
     		a[i] = sc.nextInt();
     	}
     	int z = 0;
     	ArrayList<Integer> pos = new ArrayList<Integer>();
     	ArrayList<Integer> neg = new ArrayList<Integer>();
     	for(int i=0;i<n;i++){
     		if(a[i] - (i+1)>0){
     			pos.add(a[i] - (i+1));
     		}
     		else if(a[i] - (i+1)<0){
     			neg.add((int)Math.abs(a[i]-(i+1)));
     		}
     		else{
     			z++;
     		}
     	}
     	Collections.sort(pos);
     	Collections.sort(neg);
     	if(pos.size()>neg.size()+z+1){
     		b = pos.get(pos.size()-neg.size()-z-2);
     	}
     	else if(neg.size()>pos.size()+z+1){
     		b = -neg.get(neg.size()-pos.size()-z-2);
     	}
     	long ans = 0;
     	for(int i=0;i<n;i++){
     		ans += (long)Math.abs(a[i]-(b+i+1));
     	}
     	System.out.println(ans);
    }
}