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: Accepted)

#define rep(i,x) for (int i = 0; i < x; i++)
#define mod 1000000007
#define MOD 998244353
#define inf 1e18
#define _USE_MATH_DEFINES
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#include <queue>
#include <functional>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <math.h>
#include <complex>
#include <cassert>
using namespace std;
typedef long long int ll;
typedef pair<ll, ll> p;
typedef complex<double> com;


int main(){
	int n;
	cin >> n;
	vector<int> a(n);
	rep(i, n) {
		int p;
		cin >> p;
		a[i] = p - i;
	}
	sort(a.begin(), a.end());
	ll ans = 0, sub;
	if (n % 2) {
		sub = a[(n - 1) / 2];
		rep(i, n) {
			ans += abs(a[i] - sub);
		}
		cout<<ans << endl;
	}
	else {
		sub = a[n / 2];
		rep(i, n) {
			ans += abs(a[i] - sub);
		}
		ll ans2 = 0;
		sub = a[n / 2 - 1];
		rep(i, n) {
			ans2 += abs(a[i] - sub);
		}
		cout << min(ans, ans2) << endl;
	}
	return 0;
}