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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
main()
{
  int N,*A,i,j,b,S,max=INT_MAX;
  
  scanf("%d",&N);
  A = malloc(sizeof(int)*N);
  for(i=0; i<N; i++)
  {
    scanf("%d",&b);
    A[i] = b - i;
  }
  for(i=N-1; i>0; i--)
    for(j=0; j<i; j++)
      if(A[j]<A[j])
      {
        b = A[j]; A[j] = A[j+1]; A[j+1] = b;
      }
  if(N%2==0)
    b = (A[N/2-1]+A[N/2])/2;
  else
    b = A[N/2];
  for(i=b-1; i<b+2; i++)
  {
    S = 0;
    for(i=0; i<N; i++)
      S += abs(A[i]-b);
    if(max > S)
      max = S;
  }
  printf("%d\n",max);
}