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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
int a[1234567];
long long ans1=1e15,ans2=1e15;
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL),cout.tie(NULL);
    int n;
    cin >> n;
    for(int i = 1; i <= n; i++){
    cin >> a[i];
    }
    int m1=0,m2=0;

    while(1){
            //cout<<m1<<endl;
            long long sum = 0;
    for(int i = 1; i <= n; i++){
        sum += abs(a[i] - (m1+i));
        //cout<<sum<<" ";
    }
     //cout<<" * "<<m2<<endl;
   //cout<<endl;
    if(ans1 > sum)ans1 = sum;
    else break;
    m1++;
    }
   // cout<<ans1<<endl;
    while(1){
           // cout<<m2<<endl;
            long long sum = 0;
    for(int i = 1; i <= n; i++){
        sum += abs(a[i] - (m2+i));
    //cout<<sum<<" ";
    }
   // cout<<" * "<<m2<<endl;
    if(ans2 > sum)ans2 = sum;
    else break;
    m2--;
    }
    cout<<min(ans1, ans2)<<endl;
    return 0;
}