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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
using namespace std;



int main() {
	int N, ren[200001] = {}, min = 2e9, max = 0;
	cin >> N;
	for (int i = 1; i <= N; i++) {
		cin >> ren[i];
		ren[i] -= i;
		if (ren[i] < min) min = ren[i];
		if (max < ren[i]) max = ren[i];
	}
	int result;
	for (int i = min; i <= max; i++) {
		int temp = 0;
		for (int j = 1; j <= N; j++) {
			temp += ren[j] - i < 0 ? i - ren[j] : ren[j] - i;
		}
		if (i == min || temp < result) result = temp;
		else break;
	}
	cout << result << "\n";
	return 0;
}