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.

Examples

Input

5
2 2 3 5 5


Output

2


Input

9
1 2 3 4 5 6 7 8 9


Output

0


Input

6
6 5 4 3 2 1


Output

18


Input

7
1 1 1 1 2 3 4


Output

6
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);
        boolean isBi = N / 2 * 2 == N;
        int medianBigIdx = N / 2;
        int medianBig = Ami[medianBigIdx];
        int medianSmallIdx = !isBi ? N / 2 : N / 2 - 1;
        int medianSmall = Ami[medianSmallIdx];
        long sumBig = 0, sumSmall = 0;
        for(int i = 0; i < Ami.length; i++) {
            if(Ami[i] < medianBig) {
                sumBig += medianBig - Ami[i];
            }
            else {
                sumBig += Ami[i] - medianBig;
            }

            if(Ami[i] < medianSmall) {
                sumSmall += medianSmall - Ami[i];
            }
            else {
                sumSmall += Ami[i] - medianSmall;
            }
        }
        long res = sumBig < sumSmall ? sumBig : sumSmall;
        System.out.println(res);
    }

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