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: Wrong Answer)

#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
#include <array>
#include <unordered_set>
#include <unordered_map>
#include <map>
#include <math.h>
#include <queue>
#include <stdio.h>
using namespace std;
using i64 = int64_t;
#define rep(i, n) for(int i=0;i<n;++i)
#define rep2(i, x, n) for(int i=x;i<n;++i)
#define INF 1<<29;


int main()
{
    int n;
    cin >> n;
    vector<int> a(n);
    rep(i,n) cin >> a[i];
    vector<int> d(n);
    rep(i,n) d[i] = (a[i]-(i+1));
    double avg = 0;
    rep(i,n) avg += (double)d[i]/n;
    int b = round(avg) - 5;
    i64 min_sum = INF;
    rep(i,10)
    {
        i64 sum = 0;
        rep(j,n) sum += abs(a[j]-(b+j+1));
        min_sum = min(min_sum, sum);
        b++;
    }
    
    cout << min_sum << endl;
    return 0;
}