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>
#include <math.h>
#include <stdbool.h>
#include <string.h>
#include <math.h>


int min(int a ,int b){
  if(a<b){
    return a;
  }
  return b;
}


int main(){
  int b,i,j,l,p,n,mi=0,m=0,k=0,o=0,sad=0;
  int a[300002]={};
  scanf("%d",&n);
  /*for (int j = -1000000000; j < 1000000000; j++) {
    c[j+1000000000]=j;
  }
  c[2000000010]={}
  */
  for(i=1;i<=n;i++){
    scanf("%d",&a[i]);
    m+=a[i]-i;
  }
  m=m/n;
  for(j=1;j<=n;j++){
    k+=abs(a[j]-m-j);
  }
  for(l=1;l<=n;l++){
    sad+=abs(a[l]-(m+1)-l);
  }
  for(p=1;p<=n;p++){
    o+=abs(a[p]-(m-1)-p);
  }
  sad=min(k,sad);
  sad=min(o,sad);
  printf("%d",sad);
  return 0;
}