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 <iostream>
#include <stdio.h>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include <iomanip>
#include <queue>
#include <deque>
#include <map>
#include <unordered_map>
#define rep(i,n) for(int i=0;i<n;i++)
#define repn(i,n) for(int i=1;i<=n;i++)
using namespace std;
typedef long long ll;

ll N;
ll A[200000];

int main(){
    cin>>N;
    rep(i,N){
        cin>>A[i];
        A[i]-=i+1;
    }

    sort(A,A+N);

    ll b1,b2,b3;
    if(N%2==0){
        b1=(A[N/2]+A[N/2+1])/2;
        b2=b1-1;
        b3=b1-1;
    }else{
        b1=A[N/2];
        b2=b1-1;
        b3=b1-1;
    }

    ll ans1=0, ans2=0, ans3=0;
    rep(i,N){
        ans1+=abs(A[i]-b1);
        ans2+=abs(A[i]-b2);
        ans3+=abs(A[i]-b3);
    }

    ll ans=min(ans1,min(ans2,ans3));
    cout<<ans<<endl;
}