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)

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <cmath>
#include <queue>
#include <limits>

#define ll long long

using namespace std;

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

	int n; cin >> n;
	vector<ll>v(n);
	vector<ll>sum1(n);
	vector<ll>sum2(n);

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

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

	for (int i = 0; i < n; i++) {
		sum1[i] += v[i];
		if (i > 0) sum1[i] += sum1[i - 1];
	}

	for (int i = n - 1 ; i >= 0 ; i--) {
		sum2[i] += v[i];
		if (i < n - 1) sum2[i] += sum2[i + 1];
	}

	ll ans = numeric_limits<ll>::max();

	for (int i = 0; i < n - 1; i++) {
		ll l = (i + 1), r = n - (i + 1);
		ll val = v[i] * l - sum1[i] + sum2[i + 1] - v[i] * r;
		ans = min(ans, val);
	}

	ll val = v[n - 1] * n - sum1[n - 1];
	ans = min(ans, val);

	cout << ans;

}