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: Time Limit Exceeded)


import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long[] a = new long[n + 1];
		long plus = 0;
		long minus = 0;
		long zero = 0;
		for(int i = 1; i < n + 1; i++) {
			a[i] = sc.nextLong() - i;
			if(a[i] > 0) {
				plus++;
			} else if(a[i] == 0) {
				zero++;
			} else {
				minus++;
			}
		}
		while((zero < minus || zero < plus) && plus != minus) {
			if(plus > minus) {
				for(int i = 1; i < n + 1; i++) {
					a[i]--;
				}
			} else {
				for(int i = 1; i < n + 1; i++) {
					a[i]++;
				}
			}
		}
		long ans = 0;
		for(int i = 1; i < n + 1; i++) {
			ans += Math.abs(a[i]);
		}
		System.out.println(ans);
	}

}