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 MAXN = 100005;
const ll INF = (ll)1e9;
int n;
ll a[MAXN];

ll f(int b) {
    ll c_ans = 0;
    for (int i = 0; i < n; ++i) {
        c_ans += abs(a[i] - (b + i + 1));
    }
    return c_ans;
}

int main() {
#ifdef LOCAL_PROJECT
    freopen("in.txt", "r", stdin);
    // freopen("out.txt", "w", stdout);
#endif


    cin >> n;
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
    }

    ll l = -INF, r = INF;

    while (r - l > 1) {
        ll mid = (r + l) >> 1LL;
        if (f(mid) < f(mid + 1)) {
            r = mid;
        } else {
            l = mid;
        }
        // cout << f(l) << " " << f(r) << "\n";
    }
    cout << min(f(l), f(r)) << endl;
    return 0;
}