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>

using namespace std;

int main() {
    int N;
    vector<int> A;
    cin >> N;
    A.resize(N);
    for(int i=0; i<N; i++){
        int input;
        cin >> input;
        A[i] = input;
    }

    vector<int> B;
    B.resize(N);
    for(int i=0; i<N; i++){
        B[i] = A[i] - i - 1;
    }

    sort(B.begin(), B.end());

    int num;
    if(B.size() % 2 == 0){
        num = (B[B.size() / 2 - 1] + B[B.size() / 2]) / 2;
    } else {
        num = B[B.size()/2 - 1];
    }

   int ans = 0;
   for(int i=0; i<N; i++){
       ans += abs(A[i] - (num + i));
   }

   cout << ans << endl;
}