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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		//		new Main().solveA();
		//		new Main().solveB();
		//		new Main().solveC();
		new Main().solveC2();
		// new Main().solveD();
	}

	private void solveA() {
		Scanner scanner = null;
		int numN = 0;

		try {
			scanner = new Scanner(System.in);
			numN = scanner.nextInt();

			if (numN % 2 == 0) {
				System.out.println(numN);
			} else {
				System.out.println(numN * 2);
			}

			System.out.println("");

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private void solveB() {
		Scanner scanner = null;
		int numN = 0;

		try {
			scanner = new Scanner(System.in);
			numN = scanner.nextInt();
			int[] wk = new int[numN];

			for (int i = 0; i < wk.length; i++) {
				wk[i] = scanner.nextInt();
			}
			Arrays.sort(wk);

			System.out.println(wk[wk.length - 1] - wk[0]);

			System.out.println("");

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private int getCry(int b, int currentI, int maxI, int[] wk) {
		if (currentI == maxI) {
			return 0;
		}

		return getCry(b, currentI + 1, maxI, wk) + Math.abs(wk[currentI] - (b + currentI + 1));
	}

	private void solveC2() {
		Scanner sc = new Scanner(System.in);
		int numN = sc.nextInt();
		int[] wk = new int[numN];
		for (int i = 0; i < numN; i++) {
			wk[i] = sc.nextInt() - (i + 1);
		}
		sc.close();
		Arrays.sort(wk);
		int med = numN % 2 == 0 ? numN / 2 - 1 : numN / 2;
		int b = wk[med];
		long ans = 0;
		for (int a : wk) {
			ans += Math.abs(a - b);
		}

		System.out.println(ans);
	}

	/**
	 * ⅰ)abs(xi-a)の総和(aとの距離の総和)を最小にするのは中央値で、
	 * ⅱ)(xi-a)^2の総和を最小にするのは平均値
	 */
	private void solveC() {
		Scanner scanner = null;
		int numN = 0;

		try {
			scanner = new Scanner(System.in);
			numN = scanner.nextInt();

			int[] wk = new int[numN];
			for (int i = 0; i < numN; i++) {
				wk[i] = scanner.nextInt() - (i + 1);
			}
			Arrays.sort(wk);

			//			int b = 0;
			//			if (numN % 2 == 0) {
			//				b = wk[(numN / 2) - 1];
			//			} else {
			//				b = wk[numN / 2];
			//			}

			int med = numN % 2 == 0 ? numN / 2 - 1 : numN / 2;
			int b = wk[med];

			int res = 0;

			for (int a : wk) {
				res += Math.abs(a - b);
			}
			System.out.println(res);

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private void solveD() {
		Scanner scanner = null;
		int numN = 0;
		int numK = 0;
		int numS = 0;

		try {
			scanner = new Scanner(System.in);
			numN = scanner.nextInt();

			System.out.println("");

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}
}