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 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdio>
#include <vector>
#include <iomanip>
#include <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <map>
#include <set>
#include <cmath>
using namespace std;

int main() {
    int N;
    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 cho = A.size()%2 == 0 ? (A[A.size()/2] + A[A.size()/2-1])/2 : A[A.size()/2];
    long long sum = 0;
    long long sum2 = 0;

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

    for (int i = 0; i < N; ++i) {
        sum2 += abs(cho+1 - A[i]);
    }

    cout << min(sum, sum2) << endl;

    return 0;
}