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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

int main()
{
	int i, N;
	long long A[200001];
	scanf("%d", &N);
	for (i = 1; i <= N; i++) scanf("%lld", &(A[i]));
	
	long long b = 0, ans[3] = {};
	for (i = 1; i <= N; i++) b += A[i] - i;
	b /= N;
	for (i = 1; i <= N; i++) {
		ans[0] += llabs(A[i] - b - 1 - i);
		ans[1] += llabs(A[i] - b - i);
		ans[2] += llabs(A[i] - b + 1 - i);
	}
	
	printf("%lld\n", (ans[0] < ans[1])? ((ans[0] < ans[2])? ans[0]: ans[2]): (ans[1] < ans[2])? ans[1]: ans[2]);
	fflush(stdout);
	return 0;
}