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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;

class Main{
	public static void main(String [] args){
		Input in = new Input();
		int n = in.readInt();
		int [] a = in.readArray();
		
		for(int i = 0; i < n; i++){
			a[i] -= i+1;
		}
		
		Arrays.sort(a);
		int b = a[n/2];
		
		int sum = 0;
		for(int i = 0; i < n; i++){
			int dif = a[i] - b;
			if(dif < 0){
				dif *= -1;
			}
			sum += dif;
		}
		
		System.out.println(sum);
	}
}

class Input{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	
	public String getLine(){
		String str = new String();
		try{
			str = br.readLine();
		}catch(Exception e){
			System.out.println(e);
		}
		return str;
	}
	
	public Integer readInt(){
		Integer num = -1;
		try{
			num = Integer.parseInt(br.readLine());
		}catch(Exception e){
			System.out.println(e);
		}
		return num;
	}
	
	public int [] readArray(){
		String str = new String();
		try{
			str = br.readLine();
		}catch(Exception e){
			System.out.println(e);
		}
		StringTokenizer tokens = new StringTokenizer(str, " ");
		int len = tokens.countTokens();
		int [] a = new int [len];
		for(int i = 0; i < len; i++){
			a[i] = Integer.parseInt(tokens.nextToken());
		}
		return a;
	}
	
}