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.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        String[] str_as = br.readLine().split(" ");
        int[] as = new int[n];
        //int max = -1;
        //int min = 1000000005;
        for (int i = 0; i < n; i++) {
            as[i] = Integer.parseInt(str_as[i]);
        }
        
        int ans = 0;
        int ans1 = 0;
        int ans2 = 0;
        for (int i = 0; i < n; i++) {
            ans += Math.abs(as[i] - (i+1));
        }
        for (int i = 0; i < n; i++) {
            ans1 += Math.abs(as[i] - (i+2));
        }
        for (int i = 0; i < n; i++) {
            ans2 += Math.abs(as[i] - (i));
        }
        
        int answer = 0;
        int temp = 0;
        int min = -1;
        int prev = -1;
        if (ans <= ans1 && ans <= ans2) answer = ans;
        else if (ans1 >= ans2) {
            //System.out.println("aaa");
            for (int b = 0; ; b--) {
                for (int i = 0; i < n; i++) {
                    temp += Math.abs(as[i] - (i+b));
                }
                if (b != 0 && prev < temp) {
                    answer = prev;
                    //System.out.println(b);
                    break;
                }
                prev = temp;
                temp = 0;
            }
        }
        else {
            for (int b = 2; ; b++) {
                for (int i = 0; i < n; i++) {
                    temp += Math.abs(as[i] - (i+b));
                }
                if (b != 2 && prev < temp) {
                    answer = prev;
                    break;
                }
                prev = temp;
                prev = 0;
            }
        }

        
        System.out.println(answer);
    }
}