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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws IOException {
		// TODO 自動生成されたメソッド・スタブ
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(br.readLine());
		String[] tmpArray = br.readLine().split(" ");

		int input[] = new int[n];
		long fixed[] = new long[n];

		for(int i = 0; i < n; i++){
			input[i] = Integer.parseInt(tmpArray[i]);
			fixed[i] = input[i] - (i + 1);
		}

		//debug
//		for(int i = 0; i < n; i++){
//			System.out.print(fixed[i] + " ");
//		}
//		System.out.println();

//		Arrays.sort(fixed);
		//平均を求める
		double ave = 0;
		long sum = 0;
		for(int i = 0; i < n; i++){
			ave += fixed[i];
			sum += fixed[i];
		}
//		ave /= n;
		ave = (double)sum/n;

//		System.out.println(ave);
		long d1 = -(long)Math.ceil(ave);
//		long d2 = -(long)Math.floor(ave);
		long d2 = d1 + 1;
//		long d3 = -((long)Math.ceil(ave) + 1);
		long d3 = d1 - 1;
		System.out.println(d1+ " " + d2 + " "+ d3);

		long result1 = 0;
		long result2 = 0;
		long result3 = 0;

		for(int i = 0; i < n; i++){
			result1 += Math.abs(fixed[i] + d1);
			result2 += Math.abs(fixed[i] + d2);
			result3 += Math.abs(fixed[i]);
		}

		System.out.println(Math.min(result3, Math.min(result1, result2)));

//		//最悪解
//		long result = Long.MAX_VALUE;
//		for(int b = -100 + (int)d1; b < 100 + d1 ; b++){
//			long tmpResult = 0;
//			for(int i = 0; i < n; i++){
//				tmpResult += Math.abs(fixed[i] + b);
//			}
//
//			result = Math.min(tmpResult, result);
//		}
//
//		System.out.println(result);
	}

}