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 <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main() {
	int n;
	cin >> n;
	vector<int>a(n);
	for (int i = 0; i < n; i++) {
		cin >> a.at(i);
		a.at(i) -= i + 1;
	}
	long long l = -1e18;
	long long r = 1e18;
	ll ans = 1e18;
	while (r - 1 > l) {
		long long mid = (r + l) / 2;
		bool f = true;
		ll res = 0;
		for (int i = 0; i < n; i++)res += abs(a.at(i) - mid);
		ll resl1 = 0;
		for (int i = 0; i < n; i++)resl1 += abs(a.at(i) - (mid-1));
		ll resr1 = 0;
		for (int i = 0; i < n; i++)resr1 += abs(a.at(i) - (mid+1));
		if (resl1 == res || res == resr1) {
			cout << res << endl;
			//cout << mid << " "<<resl1<<" " <<res<<" "<<resr1 << endl;
			return 0;
		}
		else if (resl1 < res && res < resr1)r = mid;
		else if (resl1 > res && res > resr1)l = mid;
		else if (resl1 > res && res < resr1) {
			cout << res << endl;
			//cout << mid << " " << resl1 << " " << res << " " << resr1 << endl;
			return 0;
		}
	}
}