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 <bits/stdc++.h>
#define int long long
using namespace std;
const int INF = 1e9 + 7, MOD = 1e9 + 7;
const long long LINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
signed main() {
	int n;
	cin >> n;
	int a[n], Sum = 0;
	map<int, int> mp;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		a[i] -= i + 1;
		mp[a[i]]++;
	}
	int Max = -LINF, Tmp;
	if (mp.size() == n) Tmp = 0;
	else {
		for (auto e : mp) {
			Max = max(Max, e.second);
			if (Max == e.second) Tmp = e.first;
		}
	}
	// cout << Tmp << endl;
	// for (int i = 0; i < n; i++) {
	// 	cout << a[i] << " ";
	// }
	// cout << endl;
	int Ans = 0;
	for (int i = 0; i < n; i++) {
		Ans += abs(a[i] - Tmp);
		// cout << abs(a[i] - Tmp) << " ";
	}
	cout << Ans << endl;
	return 0;
}