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 <algorithm>
#include <iostream>
#include <vector>
#include <map>
#include <unordered_map>
#include <cmath>

using namespace std;
typedef long long ll;
#define INF int(1e9)
#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define REPR(i, n) for(int i = n - 1; i >= 0; i--)
#define REPONE(i, n) for(int i = 1; i <= (int)(n); i++)
#define EACH(i, mp) for(auto i:mp)
#define FOR(i, m, n) for(int i = m;i < n;i++)


const int MAX_N = 2 * (int) 1e5;
int N, A[MAX_N], A1[MAX_N];
ll sum = 0;

void solve() {
    int b = sum / N;
    int ans = 0, ans1 = 0;
    REP(i, N) ans += abs(A[i] - (i + 1) - b);
    REP(i, N) ans1 += abs(A[i] - (i + 1) - (b + 1));
    cout << min(ans, ans1) << endl;
}

int main() {
    cin >> N;
    REP(i, N) {
        cin >> A[i];
        A1[i] = A[i] - (i + 1);
        sum += A1[i];
    }
    solve();
    return 0;
}