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>
using namespace std;
typedef long long ll;
int main()
{
    ll n;
    cin>>n;
    vector<ll>a;
    for(int i=0;i<n;i++)
    {
        int c;
        cin>>c;
        a.push_back(c);
    }
    for(int i=0;i<n;i++)
    {
        a[i]-=(i+1);
    }
    sort(a.begin(),a.end());
    if(n%2==1)
    {
        int h = a[n/2];
        ll ans = 0;
        for(int i=0;i<n;i++)
        {
            ans += abs(a[i]-h);
        }
        cout<<ans<<endl;
    }
    else
    {
        int h = (a[n/2-1]+a[n/2])/2;
        ll ans1 = 0;
        for(int i=0;i<n;i++)
        {
            ans1 += abs(a[i]-h);
        }
        h = (a[n/2+1]+a[n/2])/2;
        ll ans2 = 0;
        for(int i=0;i<n;i++)
        {
            ans2 += abs(a[i]-h);
        }
        cout<<min(ans1,ans2)<<endl;
    }
    return 0;
}