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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
#define rep(begin, i, end) for (int i = begin; i < (int)(end); i++)
#define all(v) v.begin(), v.end()
const int MOD = 1000000007;

int main()
{
    int N;
    cin >> N;
    vector<int> A(N);
    rep(0, i, N)
    {
        int a;
        cin >> a;
        A.at(i) = a - i + 1;
    }
    sort(all(A));
    ll ans = 0;
    ll ans1 = 0, ans2 = 0;
    if (N % 2 == 0)
    {
        rep(0, i, N)
        {
            ans += abs(A.at(i) - A.at(N / 2));
        }
    }
    else
    {
        rep(0, i, N)
        {
            ans1 += abs(A.at(i) - A.at(N / 2));
            ans2 += abs(A.at(i) - A.at(N / 2 + 1));
        }
        ans = min(ans1, ans2);
    }

    cout << ans << endl;
}