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.*;

import static java.lang.Math.*;

public class Main {


    public static void main(String[] args) {
        try (CustomReader in = new CustomReader()) {
            new Main().execute(in);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }


    public void execute(CustomReader in) throws IOException {
        final int N = in.readLineAsInt();
        int[] A = in.readLineAsIntArray();
        for (int i = 1; i <= N; i++) {
            A[i - 1] -= i;
        }
        Arrays.sort(A);
        int b = 0;
        if (N == 1) {
            b = A[0];
        } else if (N % 2 == 0) {
            b = (A[N / 2] + A[N / 2 - 1]) / 2;
        } else {
            b = A[N / 2 - 1];
        }
        int sad = 0;
        for (int i = 0; i < N; i++) {
            sad += Math.abs(A[i] - b);
        }
        System.out.println(sad);
    }


    static class CustomReader extends BufferedReader {
        public CustomReader() throws IOException {
            super(new InputStreamReader(System.in));
        }

        public int readLineAsInt() throws IOException {
            return Integer.parseInt(readLine());
        }

        public int[] readLineAsIntArray() throws IOException {
            String[] strArray = this.readLine().split(" ");
            int[] intArray = new int[strArray.length];
            for (int i = 0, n = strArray.length; i < n; i++) {
                intArray[i] = Integer.parseInt(strArray[i]);
            }
            return intArray;
        }

        public int[][] readAsIntMatrix(int rows, int columns) throws IOException {
            int[][] matrix = new int[rows][columns];
            for (int i = 0; i < rows; i++) {
                String[] r = this.readLine().split(" ");
                for (int j = 0; j < columns; j++) {
                    matrix[i][j] = Integer.parseInt(r[j]);
                }
            }
            return matrix;
        }

        public char[][] readAsCharMatrix(int rows) throws IOException {
            char[][] matrix = new char[rows][];
            for (int i = 0; i < rows; i++) {
                matrix[i] = this.readLine().toCharArray();
            }
            return matrix;
        }

    }

}