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.*;

public class Main {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long[] a = new long[n];
		Map<Long, Integer> hm = new HashMap<>();
		long b = 0;
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextLong() - i - 1;
			if (hm.containsKey(a[i])) {
				hm.put(a[i], hm.get(a[i]) + 1);
			} else {
				hm.put(a[i], 1);
			}
		}
		long temp = 0;
		long tempKey = 0;
		List<Long> sortedKey = new ArrayList<>();
		for (long key : hm.keySet()) {
			sortedKey.add(key);
		}
		Collections.sort(sortedKey);
		for (long key : sortedKey) {
			if (hm.get(key) == temp) {
				if(Math.abs(key) < Math.abs(tempKey)) {
					tempKey = key;
					temp = hm.get(key);
				}
			} else if (hm.get(key) > temp) {
				tempKey = key;
				temp = hm.get(key);
			}
			b = tempKey;
		}
		long ans = 0;
		for (int i = 0; i < n; i++) {
			ans += Math.abs(a[i] - b);
		}
		System.out.println(ans);
	}
}