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>

typedef long long ll;

ll score[3];
ll A[200005];

int main(){

	int N;

	scanf("%d",&N);

	int i;

	ll sum=0ll;

	for(i=0;i<N;i++){
	scanf(" %lld",&A[i]);
	sum+=A[i];
	}

	sum/=(ll)N;
	sum-=(N+1ll)/2ll;

	for(i=1;i<=N;i++){
	score[0]+=llabs(A[i-1]-(sum+(ll)i));
	}

	for(i=1;i<=N;i++){
	score[1]+=llabs(A[i-1]-(sum-1ll+(ll)i));
	}

	for(i=1;i<=N;i++){
	score[2]+=llabs(A[i-1]-(sum+1ll+(ll)i));
	}

	ll mi=score[0];
	for(i=1;i<3;i++){
		if(mi>score[i]){
			mi=score[i];
		}
	}

	printf("%lld\n",mi);

	return 0;
}