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 (Clang 3.8.0) (judge verdict: Wrong Answer)

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

#define min(X, Y) ((X) < (Y) ? (X) : (Y))

int cmp(const void *x, const void *y);

long long a[2 * 100005];

int main()
{
	long long n;
	long long s = 0;
	long long t = 0;

	scanf("%lld", &n);
	for (long long i = 1; i <= n; i++) {
		scanf("%lld", &a[i]);

		a[i] -= i;
	}

	qsort(a + 1, n, sizeof(long long), cmp);
	
	for (long long i = 1; i <= n; i++) {
		s += llabs(a[i] - a[n / 2]);
	}
	for (long long i = 1; i <= n; i++) {
		t += llabs(a[i] - a[(n - 1) / 2]);
	}

	printf("%lld\n", min(s, t));

	return 0;
}

int cmp(const void *x, const void *y)
{
	if (*(long long *)x > *(long long *)y) {
		return 1;
	} else if (*(long long *)x == *(long long *)y) {
		return 0;
	} else {
		return -1;
	}
}