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 rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define debug(x) cerr << #x << " = " << x << "\n"
#define debugv(x) rep(i, x.size()) cerr << x[i] << (i == x.size() - 1 ? "\n" : " ")
using namespace std;
//#define int long long
typedef long long ll;
typedef pair<int, int> pii;
const int INF = ((1LL << 30) + (1LL << 29));
const int MOD = 1000000007;

//=============================
int N;
vector<int> A;
//=============================
void input()
{
    cin>>N;
    A.resize(N);
    rep(i,N){
        cin>>A[i];
    }

}
//=============================
void func() {}
//=============================
void solve()
{
    rep(i,N){
        A[i] = A[i] - (i+1);
    }

    sort(A.begin(), A.end());
    


    int b = (N%2 ? A[N/2] : (A[N/2] + A[N/2 + 1])/2);
    int ans = 0;
    for (int i = 0; i < N; ++i){
        ans += abs(A[i] - b);
    }
    cout<<ans<<endl;

}
//=============================
signed main()
{
    input();
    solve();
    return 0;
}