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>

int min(int x, int y)
{
	if(x<y) return x;
	else if(y<x) return y;
	else if(x==y) return y;
}

int abs(int x)
{
	if(x <= 0) return -x;
	else return x;
}

int main(void)
{
	int i, N, a_sum, i_sum, b, b_min1, b_min2, b_min;
	a_sum = 0;
	i_sum = 0;

	scanf("%d", &N);

	int a[N];
	int sad[N];

	for(i=0; i<N; i++) scanf("%d", &a[i]);
	for(i=0; i<N; i++) a_sum += a[i];
	for(i=1; i<N+1; i++) i_sum += i;

	
	//b=0のとき
	sad[0] = 0;	

	for(i=1; i<N+1; i++)
	{
		sad[0] += abs(a[i-1] -i);
	}

	//b>=1のとき
	for(b=0; ; b++)
	{
		sad[b+1] = 0;
		for(i=1; i<N+1; i++)
		{
			sad[b+1] += abs(a[i-1] -i -(b+1));
		}

		if(sad[b] <= sad[b+1])
		{
			b_min = sad[b];
			break;
		}
	}
	b_min1 = sad[b];

	//b<=1のとき
	for(b=0; ; b++)
	{
		sad[b+1] = 0;
		for(i=1; i<N+1; i++)
		{
			sad[b+1] += abs(a[i-1] -i +(b+1));
		}

		if(sad[b] <= sad[b+1])
		{
			b_min = sad[b];
			break;
		}
	}
	b_min2 = sad[b];

	b_min = min(b_min1, b_min2);
	printf("%d", b_min);

}