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 <iostream>
#include <cstdio>
#include <algorithm>
#include <climits>
#include <math.h>
using namespace std;
int main(){
    int n,nummax=INT_MIN,nummin=INT_MAX,ans=INT_MAX,bsum=0;
    cin>>n;
    int a[n+1];
    // int b[n+1];
    for(int i=1;i<=n;i++){
        cin>>a[i];
        // b[i]=abs(a[i]-i);
        a[i]-=i;
        // a[i]=abs(a[i]-i);
        // cout<<a[i];
        // bsum+=b[i];
        // nummax=max(nummax,a[i]);
        // nummin=min(nummin,a[i]);
    }
    // cout<<bsum<<endl;
    // for(int b=0/*nummin/*-n*/;/*b<=nummax*/1;b++){
    //     int sum=0;
    //     for(int i=1;i<=n;i++){
    //         // sum+=abs(a[i]-(b+i));
    //         sum+=abs(a[i]-(b+i));//?????
    //     }
    //     // cout<<sum<<endl;
    //     if(ans>=sum){
    //         ans=sum;
    //     }else{
    //         break;
    //     }
    // }
    sort(&a[1],&a[n]);
    int b=a[n/2];
    int sum=0;
    for(int i=1;i<=n;i++){
        sum+=abs(a[i]-b);
    }
    ans=sum;
    sum=0;
    for(int i=1;i<=n;i++){
        sum+=abs(a[i]-b);
    }
    ans=min(ans,sum);
    sum=0;
    for(int i=1;i<=n;i++){
        sum+=abs(a[i]-b);
    }
    ans=min(ans,sum);

    cout<<ans<<endl;
}