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);
		// 整数の入力
		int a = sc.nextInt();
		List<Integer> list = new ArrayList<>();
		// スペース区切りの整数の入力
		int count = 0;
		int result = 0;
		for(int i=1;i<=a;i++){
			list.add(sc.nextInt());
			int samis =	list.get(i-1) - i;
			// System.out.println(samis);
			result = result + Math.abs(list.get(i-1) - i);
			if(samis<0){
				count++;
			}
		}
		if(count <= a/2){
			System.out.println(result);

		}else{
			// System.out.println("多い"+count);
			result = 0;
			int b=0;
			int preResult = 0;
			while(count > a/2){
				preResult = result;
				result = 0;
				count = 0;
				// System.out.println("list");
				for(int i=1;i<=a;i++){
					int samis =	list.get(i-1) - i +b;
					// System.out.println(samis);
					result = result + Math.abs(samis);
					// System.out.println(samis);
					if(samis<0){
						count++;
					}
				}
				// System.out.println("list end");
				// System.out.println(b);
				// System.out.println(count);
				// System.out.println(result);
				b++;
			}
			// System.out.println("finish");
			// System.out.println(b);
			// System.out.println(count);
			System.out.println(Math.min(result,preResult));
		//bを足すごとに値が小さいなら結果が小さくなる
		// b=0のパターンなら、上記の値-iの合計値になる
			//-1-1-1-1-1-1とかだと足したくあんる
			//負のところが半分より少なくなったタイミングでおわり

		}
	}
}