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: Accepted)

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

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 = Integer.parseInt(in.readLine());
        int[] A = in.readLineAsIntArray();

        for (int i = 0; i < N; i++) {
            A[i] -= i + 1;
        }
        Arrays.sort(A);
        int k = N / 2;

        int med = (N % 2 == 0) ? (A[k - 1] + A[k]) / 2 : A[k];

/*        long minS = S(A, A[k]);
        if (N > 1) {
            minS = Math.min(minS, S(A, A[k + 1]));
            minS = Math.min(minS, S(A, (A[k] + A[k + 1]) / 2));
        }
        */
        System.out.println(S(A, med));

    }

    private long S(int[] a, int b) {
        long s = 0L;
        for (int i = 0; i < a.length; i++) {
            s += Math.abs(a[i] - b);
        }
        return s;
    }

    static class CustomReader extends BufferedReader {

        // private static final int DEFAULT_BUF_SIZE = 2048;
        // private static final int DEFAULT_BUF_SIZE = 4096;
        // private static final int DEFAULT_BUF_SIZE = 8192;
        private static final int DEFAULT_BUF_SIZE = 16384;

        // private static final int DEFAULT_BUF_SIZE = 1048576;

        public CustomReader() throws IOException {
            super(new InputStreamReader(System.in), DEFAULT_BUF_SIZE);
        }

        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;
        }
    }

}