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 compare_int(const void *a, const void *b){
	return *(int*)a - *(int*)b;
}
int main(void){
	int N;
	scanf("%d",&N);
	int A[N];
	int B[N];
	int i;
	for(i=0;i<N;i++){
		scanf("%d",&A[i]);
		B[i] = (A[i]-i-1);
	}
	
	qsort(B,N,sizeof(int),compare_int);
	int b = B[0];
	i=0;
	while(B[i] < 0){ i++;}
	int c = B[i];

	int sum=0,sum2=0;
	for(i=0;i<N;i++){
		sum += abs(A[i]-(b+i+1));
		sum2 += abs(A[i]-(c+i+1));
	}
	if(sum > sum2) printf("%d",sum2);
	else		printf("%d",sum);
	
	return 0;
}