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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <queue>
#include <set>
#include <map>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 2e5 + 7;
const int Inf = 1e9 + 7;
typedef long long ll;
typedef pair <int, int> pr;
map <int, int> mp;
set <int> sst;
vector <int> vect;
priority_queue <pr> qua;
int n;
int a[maxn];
int c[maxn], d[maxn];

int main() {
	cin >> n;
	for(int i = 1; i <= n; i++) cin >> a[i];
	ll sum = 0;
	ll b;
	for(int i = 1; i <= n; i++) c[i] = a[i];
	for(int i = 1; i <= n; i++) d[i] = i;
	sort(c + 1, c + n + 1);
	sort(d + 1, d + n + 1);
	ll mid1 = 0, mid2 = 0;
	if(n & 1) {
		mid1 = c[n / 2 + 1];
		mid2 = d[n / 2 + 1];
		b = mid1 - mid2;
	}
	else {
		mid1 = c[n / 2] + c[n / 2 + 1];
		mid2 = d[n / 2] + d[n / 2 + 1];
		b = mid1 - mid2;
		b /= 2;
	}
	for(int i = 1; i <= n; i++) sum += abs(a[i] - (b + i));
	cout << (ll)sum << endl;
}