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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <tuple>
#include <cmath>
#include <queue>
#include <map>
#include <cmath>


using namespace std;


int main()
{
  int N, M;
  cin >> N ;
  vector<int> a(N);

  for(int i=0;i<N;i++)
    {
      cin >>a[i];
    a[i] -= (i+1);
    }

  sort(a.begin(),a.end());
  
  int c=0;
  int b;
  if (N%2==0){
    b=  (a[N / 2] + a[N/ 2 - 1]) / 2. ;
  }else{
    b = a[N/2];
  }



  for(int i=0;i<N;i++){
    c+= abs( a[i] - b);
  }
  
  

  cout << c << endl;

  return 0;
}