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;

using ll = long long;

const int N = 1e5 + 5;

int arr[N];
int n;

ll get_min(int b) {
    ll res = 0;
    for (int i = 0; i < n; ++i) {
        res += abs(arr[i] - b);
    }
    return res;
}

int solve() {
    cin >> n;
    for (int i = 0; i < n; ++i) {
        scanf("%d", &arr[i]);
        arr[i] -= i + 1;
    }
    int l = -1e9, r = 1e9;
    while (r - l > 2) {
        int ml = l + (r - l) / 3;
        int mr = r - (r - l) / 3;
        if (get_min(ml) < get_min(mr)) {
            r = mr;
        } else {
            l = ml;
        }
    }
    cout << min(get_min(l + 1), min(get_min(l), get_min(r))) << endl;


    return 0;
}

int main() {
#ifdef LOCALHOST
    freopen("input", "r", stdin);
#endif
    while (solve());

    return 0;
}