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>

#include <cstdlib>  // abs() for integer 絶対値求めやつ

#include <cmath>    // abs() for float, and fabs()

#include <algorithm>
#include <vector>
#include <string>
#define rep(i,n) for(int i = 0; i< (n);i++)

#define SORT(a) sort((a).begin(),(a).end());

#define che(a,string) cout<<string<<":"<<(a)<<endl;

#define ch(a,string) cout<<string<<":"<<(a)<<" ";

using namespace std;

typedef pair<int,int> p;

int main(){
	int n;
	cin>>n;
	vector<long long> A(n);

	rep(i,n){
	  cin>>A[i];
	  A[i]-=i+1;
	 // ch(A[i],"A[i]");

	  }
	long long sum=0;
	rep(i,n){
		sum+=A[i];
	  }
	  //ch(sum,"sum");
	  long long k = sum/n;//これをbとする！！
	  long long K = k+1; //これもb.kで計算したのと、Kで計算したの、小さいほうを出力する。
	 // ch(k,'k');
	  //ch(K,'K');
	  long long B,C;
	  B=0;C=0;
	  rep(i,n){
		  B+=abs(A[i]-k);
		  C+=abs(A[i]-K);
		}
		long long ans =min(B,C);
		cout<<ans <<endl;
		  }