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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

class Main {
	public static void main(String args[]) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		Solver solver = new Solver();
		solver.init();
		solver.readHead(in.readLine());
		for (; solver.hasNext();) {
			solver.readBody(in.readLine());
		}
		solver.solve();
	}
}

class Solver {
	int N;
	int cnt;

	public void init() {
		N = 0;
		cnt = 0;
	}

	public void readHead(String str) {
		String[] strArr = str.split(" ");
		N = Integer.parseInt(strArr[0]);
		// System.out.println(N);
		A = new int[N];
	}

	public boolean hasNext() {
		// return cnt < N;
		return cnt < 1;
	}

	public void readBody(String str) {
		// System.out.println(str);
		String[] strArr = str.split(" ");
		for (int i = 0; i < N; i++) {
			A[i] = Integer.parseInt(strArr[i]);
		}
		cnt++;
	}

	int[] A;

	public void solve() {
		long sum = 0;
		for (int i = 0; i < N; i++) {
			sum += (A[i] - i - 1);
		}
		long b1 = sum / N;
		long ans1 = 0;
		for (int i = 0; i < N; i++) {
			ans1 += Math.abs(A[i] - (b1 + i + 1));
		}
		long b2 = b1;
		if (sum < 0)
			b2--;
		else
			b2++;
		long ans2 = 0;
		for (int i = 0; i < N; i++) {
			ans2 += Math.abs(A[i] - (b2 + i + 1));
		}
		if (ans1 < ans2)
			System.out.println(ans1);
		else
			System.out.println(ans2);

	}
}