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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include<vector>
#include<climits>
#include<algorithm>
#include<bitset>
#include<cmath>
#include<functional>
#include <numeric>
#define FORi(N) for(int i=0;i<N;++i)
using namespace std;
using ll = long long;
ll gcd(ll m,ll n){
  if(n==0)return abs(m);
  return(gcd(n,m%n));
}
int main(){
  ll N;
  cin>>N;
  vector<ll> A(N);
  FORi(N){
    cin>>A[i];
    A[i]-=1+i;
  }
  sort(A.begin(),A.end());
  ll ans = 0;
  ll num = A[N/2];
  FORi(N){ans+=abs(A[i]-num);}
  ll ans_=0;
  cout<<ans<<endl;
  return 0;
}