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 <bits/stdc++.h>

using namespace std;

int main(){
    int n,total=0,dif=0;
    cin >>n;
    vector<int> a(n),b(n);
    int ans = 2*pow(10,14);
    for(int i=0;i<n;i++){
        cin >> a[i];
        b[i] = i;
    }
    if(accumulate(a.begin(),a.end(),0)>=accumulate(b.begin(),b.end(),0)){

        while(1){
            for(int h=0;h<n;h++){
                total += abs(a[h]-h-dif);
            }
            if(ans<total){
                cout << ans <<endl;
                return 0;
            }
            dif++;
            ans = total;
            total =0;
        }
    }else{

        while(1){
            for(int h=0;h<n;h++){
                total += abs(a[h]-h+dif);
            }
            if(ans<total){
                cout << ans <<endl;
                return 0;
            }
            dif++;
            ans = total;
            total =0;
        }
    }
}