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 <bits/stdc++.h>
#define MOD 1000000007
#define INF 1000000000
#define LINF 1000000000000000000
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define bit(n) (1LL<<(n))
using namespace std;

typedef pair<int, int> P;
typedef pair<long long, long long> LLP;

int main() {
    int N;
    cin >> N;
    vector<int> A(N), B(N);
    rep(i,N) {
        cin >> A[i];
        B[i] = A[i] - i;
    }

    sort(B.begin(), B.end());

    int b = N % 2 == 1 ? B[N / 2] : (B[N / 2 - 1] + B[N / 2]) / 2;
    long long ans = 0;
    rep(i,N) ans += abs(B[i] - b);

    cout << ans << endl;

    return 0;
}