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: Accepted)

import java.util.*;
import java.util.stream.Collectors;
import java.io.*;
import java.nio.charset.StandardCharsets;

public class Main {
	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		Main ins = new Main(in);
		ins.calc();
		ins.showResult();
	}

	int N;
	long[] A;

	Main(BufferedReader in) throws IOException {
		N = Integer.parseInt(in.readLine());
		A = new long[N];
		String[] tokens = in.readLine().split(" ");
		for (int i = 0; i < N; ++i) {
			A[i] = Long.parseLong(tokens[i]) - (long) (i + 1);
		}
		Arrays.sort(A);
		long med = getMedium();

		long result = Long.MAX_VALUE / 2;
		for (long b = med - 5; b <= med + 5; ++b) {
			result = Math.min(result, sub(b));
		}
		System.out.println(result);
	}

	long getMedium() {
		if (A.length == 1) {
			return A[0];
		} else if (A.length % 2 == 1) {
			return A[A.length / 2];
		} else {
			return (A[A.length / 2 - 1] + A[A.length / 2]) / 2;
		}
	}

	long sub(long b) {
		long result = 0;
		for (int i = 0; i < N; ++i) {
			result += Math.abs(A[i] - b);
		}
		return result;
	}

	void calc() {
	}

	void showResult() {
	}
}