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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; i < (n); i++)
using namespace std;
using ll = long long;

int main(){
    cin.tie(0)->sync_with_stdio(false);

	int n; cin >> n;
	vector<int> a(n);
	REP(i, n) cin >> a[i];

	int cnt = 1;
	int maxi = 0;
	int l, r;
	l = r = 0;
	REP(i, n - 1) {
		if (a[i + 1] - a[i] == 1) {
			cnt++;
			if (cnt > maxi) {
				r = i + 1;
				maxi = cnt;
			}
		} else cnt = 1;
	}
	l = max(0, r - maxi + 1);
	// cout << maxi << " l:" << l << " r:" << r << '\n';

	vector<int> b(n, 0);
	for (int i = l; i <= r; i++)
		b[i] = a[i];
	if (l == 0 && r == 0)
		REP(i, n) b[i] = i + 1;
	else {
		for (int i = r + 1; i < n; i++)
			if (i - 1 >= 0)
				b[i] = b[i - 1] + 1;
		for (int i = l - 1; i >= 0; i--)
			if (i >= 0)
				b[i] = b[i + 1] - 1;
	}
	// REP(i, n) cout << a[i] << ' ';
	// cout << '\n';
	// REP(i, n) cout << b[i] << ' ';
	// cout << '\n';

	ll res = 0;
	REP(i, n)
		res += abs(a[i] - b[i]);
	cout << res << '\n';
    return 0;
}