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: Accepted)

#include <iostream>
#include <cmath>
#include <vector>
#include <map>
#include <cstdio>
#include <algorithm>
#include <functional>
#include <string>
#include <numeric>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;

#define rep(i, a, N) for(int i = a; i < N; i++)

int main() {
    int N;
    cin >> N;
    vector<int> A(N), B(N);

    rep(i, 0, N) {
        scanf("%d", &A[i]);
        A[i] -= i + 1;
    }

    sort(A.begin(), A.end());
    int median;
    if (N % 2 == 0) median = (A[N / 2] + A[N / 2 - 1]) / 2;
    else median = A[(N + 1) / 2 - 1];

    ll ans = 0;
    rep(i, 0, N) ans += abs(A[i] - median);

    cout << ans << endl;
}