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;
#define INF 10000000
const int maxn = 2e5+ 5;

int n;
int a[maxn];
map<int,int>mp;
int main()
{
    ios::sync_with_stdio(false),cin.tie(0);
    cin>>n;
    for(int i=1;i<=n;i++)
        {
            cin>>a[i];
            a[i]-=i;
        }
    sort(a+1,a+n+1);
    for(int i=1;i<=n;i++)
          mp[a[i]]++;
    int pos=0;
    int num=1;
    for(int i=1;i<=n;i++)
        if(mp[a[i]]>num)
        {
           num=mp[a[i]];
           pos=a[i];
        }
    ll sum=0;
    for(int i=1;i<=n;i++)
        sum+=abs(a[i]-pos);
    cout<<sum;
    return 0;
}