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: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>

#define MAX(p,q) ((p>q)?(p):(q))
#define MIN(p,q) ((p<q)?(p):(q))

#define INF 1000000000
#define REP(i,n) for(i=0;i<n;i++)

int gcd(int a,int b);

int main(void)
{
  int n;
  scanf("%d",&n);
  long a[200000],sum[200000];
  int i;
  long ans=INF;
  long min=INF,max=0;
  int j;

  REP(i,n)
  {
    scanf("%ld",&a[i]);
    a[i] -= i;
    min=MIN(min,a[i]);
    max=MAX(max,a[i]);
  }
  long median;
  median = (max+min)/2;
  for(i = median-3;i <= median+3; i++)
  {
    REP(j,n)
    {
      sum[i] += labs(a[j]-i);
    }
    ans = MIN(sum[i],ans);
  }
  printf("%ld",ans);

  return 0;
}

int gcd(int a,int b)
{
  int max,min,tmp;
  max = MAX(a,b);
  min = MIN(a,b);
  if(max%min==0) return min;
  else
  {
    tmp = min;
    min = max%min;
    max = tmp;
    return gcd(max,min);
  }
}