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>

using namespace std;
int abss(int A[],int n,int b){
    int ans=0;
    for(int i=0;i<n;i++){
        ans+=abs(A[i]-(b+i+1));
    }
    return ans;
}

int main(){

    int n;
    cin>>n;
    int A[n];
    for(int i=0;i<n;i++){
        cin>>A[i];
    }
    int b=0;
    int preans=0;
    int min;
    
    
    while(true){
        int ans=abss(A,n,b);
        if(b==0){
            preans=ans;
            b++;
        }else if(ans>preans){
            min=preans;
            break;
        }else{
            preans=ans;
            b++;
        }
    }
    //cout<<min<<endl;
    
    b=-1;
    int fmin;
    
    preans=abss(A,n,0);
    
    //cout<<preans<<endl;
    
    while(true){
        int ans=abss(A,n,b);
        
         if(preans<ans){
            fmin=preans;
             //cout<<fmin<<b<<endl;
            break;
        }else{
            preans=ans;
            
            b--;
        }
    }
    
    cout<<((min>fmin)?fmin:min)<<endl;




return 0;
}