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: Wrong Answer)

#include<iostream>
#include<algorithm>
#include<cmath>
#include<vector>
#include<queue>
#include<stack>
#include<string>
using namespace std;
typedef long long ll;
ll a[200010];
int main(){
	ll n;
	cin >> n;
	ll sum = 0;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		sum += a[i];
	}
	sum /= n;
	ll ans = 10000000000000000;
	ll b = sum;
	b -= n / 2;
	ll cnt = 0;
	int err = 0;
	for (int j = 0;; j --) {
		for (int i = 0; i < n; i++) {
			cnt += abs(a[i] - (b + i + j));
		}
		if (ans > cnt && err) {
			ans = cnt;
			break;
		}
		if (ans > cnt)ans = cnt;
		else {
			j += 101;
			err++;
		}
		if (err > 100)break;
		cnt = 0;
	}
	cnt = 0;
	err = 0;
	for (int j = 0;; j +=100) {
		for (int i = 0; i < n; i++) {
			cnt += abs(a[i] - (b + i + j));
		}
		if (ans > cnt && err) {
			ans = cnt;
			break;
		}
		if (ans > cnt)ans = cnt;
		else {
			j -= 101;
			err++;
		}
		if (err > 100)break;
		cnt = 0;
	}
	cout << ans << endl;
    return 0;
}