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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
    private static final BufferedReader input = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args) {
        exec(args);
    }

    public static void exec(String[] args) {
        String str = readLineStandardInput();
        int N = Integer.parseInt(str);
        str = readLineStandardInput();
        String[] Astr = str.split(" ");
        int[] Ami = new int[N];
        for(int i = 0; i < Ami.length; i++){
            int tmp = Integer.parseInt(Astr[i]);
            Ami[i] = tmp - (i + 1);
        }
        Arrays.sort(Ami);
        int median = Ami[N / 2];
        int sum = 0;
        for(int i = 0; i < Ami.length; i++) {
            if(Ami[i] < median) {
                sum += median - Ami[i];
            }
            else {
                sum += Ami[i] - median;
            }
        }
        System.out.println(sum);
    }

    private static String readLineStandardInput() {
        String str;
        try {
            str = input.readLine();
        } catch(IOException e){
            str = null;
            System.out.println(e);
        }
        return str;
    }
}