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.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = Integer.parseInt(in.nextLine());
		List<Long> nums = new ArrayList<>(n);
		String[] tokens = in.nextLine().split(" ");
		for (int i = 0; i < n; ++i) {
			nums.add(Long.parseLong(tokens[i]));
		}
		// bを0としたときの差分分布をとる
		Map<Long, Integer> count = new HashMap<>();
		for (int i = 0; i < n; ++i) {
			long diff = nums.get(i) - (i + 1);
			if (!count.containsKey(diff)) {
				count.put(diff, 1);
			} else {
				count.put(diff, count.get(diff) + 1);
			}
		}
		// 最大のカウントを取得する
		int maxCount = Integer.MIN_VALUE;
		long target = 0;
		for (Long key : count.keySet()) {
			//System.out.println("diff: " + key + ", count: " + count.get(key));
			if (maxCount < count.get(key)) {
				maxCount = count.get(key);
				target = key;
			}
		}
		long b = target;
		long result = 0;
		for (int i = 0; i < n; ++i) {
			long diff = Math.abs(nums.get(i) - (b + i + 1));
//			System.out.println(nums.get(i) + ", " + b + ", " + diff);
			result += diff;
		}
		System.out.println(result);
		in.close();
	}

}