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 ll long long
using namespace std;

int main() 
{
    int n;
    cin >> n;
    vector<int> v;
    for (int i=0; i<n; i++)
    {
        int a;
        cin >> a;
        v.push_back(a-i-1);
    }
    int sum = 0;
    map<int, int> mp;
    for (int i=0; i<n; i++)
        mp[v[i]]++;
    int maxx = 0, el;
    for (auto x:mp)
    {
        if (x.second > maxx)
        {   
            el = x.first;
            maxx = x.second;
        }
    }
    int el2=0;
    for (int i=0; i<n; i++)
    {
        el2 += v[i];
    }
    if (maxx == 1)
        el = el2;
    for (int i=0; i<n; i++)
    {
        sum += abs(v[i]-el);
        // cout << v[i] << " ";
    }
    cout << sum;
    return 0;
}