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.

Examples

Input

5
2 2 3 5 5


Output

2


Input

9
1 2 3 4 5 6 7 8 9


Output

0


Input

6
6 5 4 3 2 1


Output

18


Input

7
1 1 1 1 2 3 4


Output

6
#include<bits/stdc++.h>
using namespace std;
#define ll long long
int main(){
  ll n,c=0;
  cin>>n;
  vector<ll> a(n),b(n);
  for(ll i=1;i<=n;i++){
    cin>>a[i-1];
    b[i-1]=a[i-1]-i;
  }
  sort(b.begin(),b.end());
  ll bb;
  if(n%2==1){
    bb=b[n/2];
  }else{
    bb=(b[n/2]+b[n/2-1])/2;
  }
  for(ll i=0;i<n;i++){
    c+=abs(b[i]-bb);
  }
  cout<<c;
}
