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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <string>
#include <sstream>
#include <complex>
#include <vector>
#include <list>
#include <queue>
#include <deque>
#include <stack>
#include <map>
#include <set>
#include <numeric>

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

using namespace std;
typedef long long unsigned int ll;

int calc_sad(vector<int> A, int b) {
    int sad = 0;
    rep(i, A.size()) {
        sad += abs(A[i] -b);
    }
    return sad;
}

int main() {
    int N;
    vector<int> A;
    cin >> N;
    rep(i, N) {
        int a;
        cin >> a;
        a -= i + 1;
        A.push_back(a);
    }

    int b = round(accumulate(A.begin(), A.end(), 0) / A.size());

    int result = calc_sad(A, b);

    cout << result << endl;
    return 0;
}