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>
#define pb push_back
#define all(a) a.begin(), a.end()
#define sz(a) (int)a.size()
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int>pii;
const int maxn=2e5+100;
ll n, arr[maxn];
int main()
{
    ios_base::sync_with_stdio(false), cin.tie(0);
    cin>>n;
    for(int i=1; i<=n; ++i)
        cin>>arr[i];
    ll sum=0;
    vector<int>v;
    for(int i=1; i<=n; i++)
    {
        v.pb(arr[i]-i);
        sum+=abs(arr[i]-i);
    }
    sort(all(v));
    ll val=0;
    if(n%2==0)val=(v[n/2]+v[n/2-1])/2;
    else val=v[n/2];
    cout<<min(abs(sum-val*n), abs(sum+val*n))<<"\n";
    return 0;
}