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.Arrays;
import java.util.Scanner;
public class Main {
	
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] map = new int[N];
		int totalP = 0;
		int countP = 0;
		int totalN = 0;
		int countN = 0;
		int countZ = 0;
		for (int i = 0; i < N; i++) {
			map[i] = sc.nextInt() - (i + 1);
			if (map[i] > 0) {
				totalP += map[i];
				countP++;
			} else if (map[i] < 0) {
				totalN += map[i];
				countN++;
			} else {
				countZ++;
			}
		}
		
		//input3 OK
		if (totalP == Math.abs(totalN)) {
			System.out.println(totalP * 2);
			return;
		}
		
		Arrays.sort(map);
		
		if (countP > countN) {
			int start = Arrays.binarySearch(map, 0);
			start = start < 0 ? Math.abs(start + 1) : start;
			
			float total = 0F;
			int totalC = 0;
			for (int i = start; i < N; i++) {
				total += map[i];
				totalC++;
			}
			int val = Math.round(-total / totalC);
			
			if (val <= countZ) {
				val = 0;
			} else {
				val = -val;
			}
			
			int ans = 0;
			for (int i = 0; i < N; i++) {
				ans += Math.abs(map[i] + val);
			}
			System.out.println(ans);
		} else {
			int start = Arrays.binarySearch(map, 0);
			start = start < 0 ? Math.abs(start + 1) - 1 : start - 1;
			
			float total = 0F;
			int totalC = 0;
			for (int i = start; i >= 0; i--) {
				total += map[i];
				totalC++;
			}
			int val = Math.round(Math.abs(total / totalC));
			
			if (val <= countZ) {
				val = 0;
			}
			
			int ans = 0;
			for (int i = 0; i < N; i++) {
				ans += Math.abs(map[i] + val);
			}
			System.out.println(ans);
		}
	}
}