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 (Clang 3.8.0) (judge verdict: Accepted)

#include <fstream>
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <queue>
#include <set>
#include <cmath>
#include <tuple>
#include <sstream>
#include <iomanip>
#include <map>
#include <unordered_map>

#define rep(i,n) for (int i = 0; i < (n); ++i)
#define sz(x) int(x.size())

using namespace std;
typedef long long ll;

int main(int argc, const char * argv[]) {
    //    ifstream in("input.txt");
    //    cin.rdbuf(in.rdbuf());
    
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int n;
    cin >> n;
    
    vector<int> a(n);
    rep(i, n)
    {
        cin >> a[i];
        a[i] -= i + 1;
    }
    
    sort(a.begin(), a.end());
    
    int b = a[n/2];
    
    ll ans = 0;
    rep(i, n)
    {
        ans += abs(a[i] - b);
    }
    
    cout << ans << endl;
    
    return 0;
}