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>
using namespace std;
typedef int64_t int64;
typedef uint32_t uint;
typedef uint64_t uint64;

template<typename T>
T v_max(const vector<T>& vec){
    T max=vec[0];
    for(uint i=1; i<vec.size(); ++i){
        if(vec[i]>max){ max=vec[i]; }
    }
    return max;
}
template<typename T>
T v_min(const vector<T>& vec){
    T min=vec[0];
    for(uint i=1; i<vec.size(); ++i){
        if(vec[i]<min){ min=vec[i]; }
    }
    return min;
}

int64 sad(const vector<int>& vA, int b){
    int64 sum=0ll;
    for(uint vi=0; vi<vA.size(); ++vi){
        sum += abs(vA[vi] - b);
    }
    return sum;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    
    int N; cin >> N;
    
    vector<int> vA(N);
    for(int i=0; i<N; ++i){
        int a; cin >> a;
        vA[i] = a-(i+1);
    }
    
    int64 min=v_min(vA);
    int64 max=v_max(vA);
    /*
    int64 min_sad=sad(vA, minn);
    for(int64 i=min+1; i<=max; ++i){
        int64 tmp=sad(vA, i);
        if(tmp < min_sad){ min_sad=tmp; }
    }
    cout << min_sad << endl;
    //*/
    
    // binary search
    int64 sadVal_prev=sad(vA, min);
    while(max-min>1){
        int64 mid = (max+min)/2;
        int64 sadVal=sad(vA, mid);
        if(sadVal<sadVal_prev){
            min = mid;
            sadVal_prev = sadVal;
        }else{
            max = mid;
        }
    }
    int64 sad_min = sad(vA, min);
    int64 sad_max = sad(vA, max);
    if(sad_min<sad_max){
        cout << sad_min << endl;
    }else{
        cout << sad_max << endl;
    }
    
    return 0;
}