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;
#define rep(i,n) for(int i=0;i<int(n);++i)
#define all(a) a.begin(),a.end()
typedef long long ll;

int n;
vector<ll> a;

ll calc(ll x){
    ll res = 0;
    rep(i,n){
        res += abs(a[i]-x);
    }
    return res;
}

int main(void){
    cin>>n;
    a.resize(n);
    rep(i,n){
        cin>>a[i];
        a[i] -= i+1;
    }
    sort(all(a));
    ll l = a[0], r = a[n-1];
    while(l + 2 < r){
        ll m1 = (l*2+r)/3, m2 = (l+r*2)/3;
        if(calc(m1) < calc(m2)) r = m2;
        else l = m1;
    }
    cout<<min({calc(l),calc((l+r)/2),calc(r)})<<endl;
    return 0;
}