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;
const int N = 3e5 + 5;
int n, a[N];
long long get(int b) {
	long long ret = 0;
	for (int i = 0; i < n; ++i) {
		++b;
		ret += abs(a[i] - b);
	}
	return ret;
}
int main() {
#ifndef ONLINE_JUDGE
//	freopen("input.in", "r", stdin);
#endif
	scanf("%d", &n);
	for (int i = 0; i < n; ++i)
		scanf("%d", a + i);
	int lo = -2e5, hi = 1e9;
	long long res = 2e18;
	while (lo <= hi) {
		int mid = lo + (hi - lo) / 2;
		int mid_1 = mid - 1;
		long long d = get(mid), d1 = get(mid_1);
		if (d > d1) {
			hi = mid - 1;
			res = min(res, d1);
		} else {
			lo = mid + 1;
			res = min(res, d);
		}
	}
	printf("%lld\n", res);
	return 0;
}