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 _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <fstream>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <stack>
#include <string> 
#include <iomanip>
#include <list>
#include <random>
#include <numeric> //iota - iota(v.begin(), v.end(), x) x, x + 1, x + 2...

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
typedef int INT;
#define int ll
#define mmin(a, b) a = min(a, b)
#define mmax(a, b) a = max(a, b)
#define mp(a,b) make_pair(a,b)
#define pb(a) push_back(a)
#define all(a) a.begin(),a.end()
#define sz(a) ((int)(a.size()))
#define watch(x) cout << (#x) << " = " << x << endl;
#define max3(a, b, c) max(a, max(b, c))
#define min3(a, b, c) min(a, min(b, c))
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;

/*
tuple<int, string> f() {
return {485, "Hello"};
}
int a;
string b;
tie(a, b) = f();
*/

const double PI = 2 * acos(0.0), eps = 1e-8;
const int oo = 1000000000000000000;

template<class T>
void show(const vector<T> &a) {
	cout << sz(a) << endl;
	for (T x : a)
		cout << x << " ";
	cout << endl;
}

const ll M = 998244353;

ll MOD(ll a) {
	if (a >= 0) return a >= M ? a % M : a;
	if (a <= -M) a %= M;
	return a ? a + M : a;
}

int gcd(int a, int b)
{
	while (a > 0)
	{
		if (a < b)
			swap(a, b);
		a %= b;
	}
	return b;
}


/*______________________________________________________________________________________________________________________________
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int o = 1000000;

signed main()
{
	ios::sync_with_stdio(false);
	cin.tie(NULL); cout.tie(NULL);


	int n;
	cin >> n;
	vector <int> a(n);
	for (int i = 0; i < n; i++)
	{
		cin >> a[i];
		a[i] -= (i + 1);
	}

	sort(all(a));
	

	int sum = 0;
	for (int i = 0; i < n; i++)
	{
		sum += abs(a[i] - a[n / 2]); 
	}

	cout << sum;


}