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 int ll;


int main()
{
   ll n,i,j,k,l,maxx=0;
   cin>>n;
   ll a[n+1];
   for(i=1;i<=n;i++)
   {
       cin>>a[i];
       if(a[i]>maxx)
       {
           maxx=a[i];
       }
   }
   i=-maxx;
   j=maxx;
   ll ans=0;
   while(i<=j)
   {
       ll mid=(i+j)/2;
       //cout<<mid<<endl;
       ll sum1=0,sum2=0,sum3=0;
       for(ll p=1;p<=n;p++)
       {
           sum1+=abs(a[p]-(mid+p));
           sum2+=abs(a[p]-(mid+1+p));
           sum3+=abs(a[p]-(mid-1+p));
       }
       //cout<<sum1<<" "<<sum2<<" "<<sum3<<endl;
       if(sum2>=sum1 && sum3>=sum1)
       {
           ans=sum1;
           break;
       }
       else if(sum2>sum1 && sum3<sum1)
       {
           j=mid-1;
       }
       else
       {
           i=mid+1;
       }
   }
   cout<<ans<<endl;


    return 0;
}