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 cmpnum(const void * n1, const void * n2)
{
	if (*(long *)n1 > *(long *)n2)
	{
		return 1;
	}
	else if (*(long *)n1 < *(long *)n2)
	{
		return -1;
	}
	else
	{
		return 0;
	}
}

long long int fn(long long int i, long long int n, long int a[])
{
	long long int sum=0;
	long long int j;
	for(j=0;j<i;j++){
		sum+=a[i]-a[j];
		}
	for(j=i+1;j<n;j++)
		sum+=(a[j]-a[i]);
	return sum;
}

int main(void)
{
	long long int n,i,min;
	scanf("%lld",&n);
	long int a[n];
	for(i=0;i<n;i++){
		scanf("%ld",&a[i]);
		a[i]-=(i+1);
	}
	qsort(a, sizeof(a) / sizeof(a[0]), sizeof(long), cmpnum);
	min=fn(n/2,n,a);
	i=0;
	if(fn(n/2-1,n,a)<=fn(n/2,n,a)){
		while(fn(n/2-i-1,n,a)<=fn(n/2-i,n,a)){
			i++;
		}
		printf("%lld",fn(n/2-i,n,a));
		return 0;
	}
	i=0;
	if(fn(n/2+1,n,a)<fn(n/2,n,a)){
		while(fn(n/2+i+1,n,a)<=fn(n/2+i,n,a)){
			i++;
		}
		printf("%lld",fn(n/2+i,n,a));
		return 0;
	}
	printf("%lld",fn(n/2,n,a));	
	return 0;
}