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: Runtime Error)

#include<bits/stdc++.h>
#define F first
#define S second
#define endl '\n'
#define lcm( a, b ) ((a)/__gcd(a,b)*(b))
#define MP make_pair
#define pb push_back
#define all(x) (x).begin(),(x).end()

using namespace std;

typedef long long LL;
typedef pair<int, int> P;
typedef pair<int, P> i_P;
typedef pair< LL, LL > L_P;

const int INF = INT_MAX;
const int MIN = INT_MIN;
const LL LINF = LLONG_MAX;
const int MOD = 1000000000 + 7;
const int SIZE = 100005;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n;
    cin >> n;
    LL a[SIZE];
    LL a_sort[SIZE];
    for( int i = 0; i < n; ++i ) {
        cin >> a[i];
        a_sort[i] = a[i] - ( i + 1 );

    }

    sort( a_sort, a_sort + n );
    LL cent = a_sort[n / 2];

    LL res = 0;
    for( int i = 0; i < n; ++i ) {
        res += llabs( a[i] - ( i + 1 + cent ) );

    }
    cout << res << endl;

    return 0;
}