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>
using namespace std;
typedef pair<int,int> pii;
#define ll long long int
#define pb push_back
#define mp make_pair
#define boost ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define forn(i, n) for(int i = 0; i < (int)(n); i++)
#define ford(i, n) for(int i = (int)(n) - 1; i >= 0; i--)
#define F first
#define S second
#define mset(x,v) memset(x, v, sizeof(x))
#define left(x) 2*x
#define right(x) (2*x) + 1
#define ALL(t) (t).begin(),(t).end() 
#define ret return 0
#define all(x) x.begin(),x.end()
ll n;
int main()
{
    boost;
           cin>>n;
           ll arr[n+1];
           for(int i=1;i<=n;i++)
           {
                 cin>>arr[i];
                 arr[i]=arr[i]-i-1;
           }
           sort(arr+1,arr+n+1);
           ll med=arr[n/2];
           ll ans=0;
           for(int i=1;i<=n;i++)
           {
                 ans+=abs(med-arr[i]);
           }
           cout<<ans<<endl;
}