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<bits/stdc++.h>
using namespace std;
long long n,i,a[222222],b,x,b1,b2,min1,min2,min3,min4,b3;
int main()
{
    cin>>n;
    for(i=1;i<=n;i++)
    {
        cin>>a[i];
        if(i==n/2)
            b=a[i]-i;
        if(i==n/2-1)
            b1=a[i]-i;
        if(i==n/2+1)
            b2=a[i]-i;
    }
    b3=(b+b1+b2)/3;
    for(i=1;i<=n;i++)
    {
        min1+=abs(a[i]-(i+b));
        min2+=abs(a[i]-(i+b1));
        min3+=abs(a[i]-(i+b2));
        min4+=abs(a[i]-(i+b3));
    }
    cout<<min(min(min1,min2),min(min3,min4));
}