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.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        PrintWriter out = new PrintWriter(System.out);
        Scanner sc = new Scanner(System.in);
        TaskC task = new TaskC();

        task.solve(sc, out);
        out.flush();
        sc.close();
    }
    static class TaskC{
        void solve(Scanner sc, PrintWriter out){
            int N = nint(sc);
            long[] lLine = longLine(sc, N);
            long[] AminusN = new long[N];
            for (int i = 0; i < N; i++) {
                AminusN[i] = lLine[i] - (i+1);
            }
            Arrays.sort(AminusN);
            long b;
            if (N%2==0){
                b = AminusN[N/2 -1];
            }else{
                b = AminusN[(N+1)/2 -1];
            }
            long result = 0;
            for (long a: AminusN){
                result += Math.abs(a - b);
            }
            out.println(result);

        }
    }
    static int nint(Scanner sc){
        return Integer.parseInt(sc.next());
    }
    static long nlong(Scanner sc){
        return Long.parseLong(sc.next());
    }
    static double ndouble(Scanner sc){
        return Double.parseDouble(sc.next());
    }
    static float nfloat(Scanner sc){
        return Float.parseFloat(sc.next());
    }
    static String nstr(Scanner sc){
        return  String.valueOf(sc.next());
    }
    static long[] longLine(Scanner sc, int size){
        long[] lLine = new long[size];
        for (int i = 0; i < size; i++) {
            lLine[i] = nlong(sc);
        }
        return lLine;
    }
    static int[] intLine(Scanner sc, int size){
        int[] iLine = new int[size];
        for (int i = 0; i < size; i++) {
            iLine[i] = nint(sc);
        }
        return iLine;
    }
    static String[] strLine(Scanner sc, int size){
        String[] strLine = new String[size];
        for (int i = 0; i < size; i++) {
            strLine[i] = nstr(sc);
        }
        return strLine;
    }
}