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: Time Limit Exceeded)

#include<stdio.h>
#include<stdlib.h>
int main(void){
	
	int *a,c,n,i,j,t,b,k;
	int x[30000000];
	scanf("%d ",&n);
	a=(int*)malloc(sizeof(int)*n);
	for(i=0;i<n;i++){
	scanf("%d ",&a[i]);}

	k=0;
	for(i=-1000000;i<1000000;i++){t=0;
		for(j=0;j<n;j++){
			b=a[j]-i-j;
			if(b>0){
			t=b+t;}else{t=-b+t;}
				}x[k]=t;k++;		
				}
	c=0;
	for(i=0;i<k;i++){
		for(j=0;j<k;j++){
		if(x[i]<x[j]){
		c=x[i];
		x[i]=x[j];
		x[j]=c;}
		}
	}
		
	printf("%d\n",x[0]);

	free(a);


	return 0;
}