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;
typedef pair<ll, ll> P;

#define pb push_back
#define rep(i, n) for(int i = 0; i < (n); i++)
#define dep(i, a, n) for(int i = a; i >= (n); i--)
#define FOR(i, a, n) for(int i = a; i < (n); i++)
#define mod (ll)(1e9+7)
#define int ll
#define INF 1000000000

__attribute__((constructor))
void initial() {
  cin.tie(0);
  ios::sync_with_stdio(false);
}

signed main() {
	ll n, a[200002], sum = 0, maxx = 0;
  cin >> n;
  rep(i, n) {
    cin >> a[i];
    a[i] -= (i + 1);
  }
  sort(a, a + n);
  ll mid = a[n / 2];
  rep(i, n) {
    a[i] -= mid;
    sum += abs(a[i]);
  }
  cout << sum << endl;
	return 0;
}