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<math.h>
int zettai(int x,int y){
  if(x-y > 0) return x-y;
  else return y-x;
}
int main(){
  int N,i,sum,b,ans1,ans2,ans3,min;
  int A[200000];
  ans1 = 0;
  ans2 = 0;
  ans3 = 0;
  sum = 0;
  scanf("%d",&N);
  for(i=0;i<N;i++){
    scanf("%d",&A[i]);
    A[i] = A[i] - i;
    sum += A[i];
  }
  b = sum / N;
  for(i=0;i<N;i++){
    ans1 += zettai(A[i],b);
    ans2 += zettai(A[i],b-1);
    ans3 += zettai(A[i],b+1);
  }
  min = ans1;
  if(min>ans2) min=ans2;
  if(min>ans2) min=ans3;
  printf("%d\n",min);
  return 0;
}