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<iostream>
#include<vector>
typedef long long ll;
using namespace std;

ll max2(ll a,ll b){
    ll ans=a;
    if(ans<b)ans=b;
    return ans;
}
ll min2(ll a,ll b){
    ll ans=a;
    if(ans>b)ans=b;
    return ans;
}
int n;
long long calc(vector<int> const& a,int b){
    long long sum=0;
    for(int i=0;i<n;i++){
        sum+=max2(a[i]-b-i-1,b+i+1-a[i]);
    }
    return sum;
}
ll bs(vector<int> const& a){
    int max=0;
    for(int i=0;i<a.size();i++){
        if(max<a[i])max=a[i];
    }
    int left=(-1)*max-1;
    int right=max;
    int mid;
    while(right-left>1){
        mid=(left+right)/2;
        if(calc(a,mid+1)-calc(a,mid)<0)left=mid;
        else right=mid;
    }
    return min2(calc(a,left),calc(a,right));
}
int main(){
    cin>>n;
    vector<int> a(n);
    for(int i=0;i<n;i++)cin>>a[i];
    cout<<bs(a)<<endl;
    return 0;
}