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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int length = sc.nextInt();
        int sum1=0;
        ArrayList<Integer> list = new ArrayList<>();
        while(sc.hasNext()){
            int num;
            list.add((num = sc.nextInt()));
            sum1 += num;
        }
        double max = sum1/4;
        int p=0,q=0,r=0,s = 0;
        int sum = 0;
        int flag = 0;
        int prev = 0;
        for(int i = 0;i<length;i++){
            sum+=list.get(i);
            if(sum>max){
                if(i-prev == 1){
                    switch (flag){
                        case 0:
                            p = list.get(i);
                            prev = i;
                            break;
                        case 1:
                            q = list.get(i);
                            prev = i;
                            break;
                        case 2:
                            r = list.get(i);
                            s = sum1-p-q-r;
                            System.out.println(sa(p,q,r,s));
                            return;
                    }
                    sum = 0;
                }else {
                    switch (flag) {
                        case 0:
                            p = sum - list.get(i);
                            prev = i;
                            break;
                        case 1:
                            q = sum - list.get(i);
                            prev = i;
                            break;
                        case 2:
                            r = sum - list.get(i);
                            s = sum1 - p - q - r;
                            System.out.println(sa(p, q, r, s));
                            return;
                    }
                    sum = list.get(i);
                }
                flag++;
            }
        }
    }
    private static int sa(int p, int q, int r, int s){
        ArrayList<Integer> list = new ArrayList<>();
        list.add(p);
        list.add(q);
        list.add(r);
        list.add(s);
        Collections.sort(list);
        return list.get(3)-list.get(0);
    }
}