#include <iostream>
#include <bits/stdc++.h>

using namespace std;
const long long MOD = 998244353;
const long long MAXN = 300;
pair<long long,long long> arr[MAXN];
long long pw[MAXN];
int main(){
    long long n;
    cin>>n;
    pw[0] = 1;
    for(long long i=1;i<=n;i++){
        pw[i] = pw[i-1]*2;
        pw[i]%=MOD;
        cin>>arr[i].first>>arr[i].second;
    }
    long long ans = (pw[n]-n-1+MOD)%MOD;
    
    for(long long i=1;i<=n;i++){
        for(long long j=i+1;j<=n;j++){
            long long cnt = 0;
            for(long long k=j+1;k<=n;k++){
                if((arr[k].second-arr[i].second)*(arr[j].first-arr[i].first) == (arr[j].second-arr[i].second)*(arr[k].first-arr[i].first)){
                    cnt++;
                }
            }
            ans-=(pw[cnt]-MOD);
            ans%=MOD;
        }
    }
    cout<<ans<<endl;
    
}
### Prompt

Please create a solution in cpp to the following problem:

You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.

cddb0c267926c2add885ca153c47ad8a.png

For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.

For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.

Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.

However, since the sum can be extremely large, print the sum modulo 998244353.

Constraints

* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.

Input

The input is given from Standard Input in the following format:


N
x_1 y_1
x_2 y_2
:
x_N y_N


Output

Print the sum of all the scores modulo 998244353.

Examples

Input

4
0 0
0 1
1 0
1 1


Output

5


Input

5
0 0
0 1
0 2
0 3
1 1


Output

11


Input

1
3141 2718


Output

0

### Response

```cpp
#include <iostream>
#include <bits/stdc++.h>

using namespace std;
const long long MOD = 998244353;
const long long MAXN = 300;
pair<long long,long long> arr[MAXN];
long long pw[MAXN];
int main(){
    long long n;
    cin>>n;
    pw[0] = 1;
    for(long long i=1;i<=n;i++){
        pw[i] = pw[i-1]*2;
        pw[i]%=MOD;
        cin>>arr[i].first>>arr[i].second;
    }
    long long ans = (pw[n]-n-1+MOD)%MOD;
    
    for(long long i=1;i<=n;i++){
        for(long long j=i+1;j<=n;j++){
            long long cnt = 0;
            for(long long k=j+1;k<=n;k++){
                if((arr[k].second-arr[i].second)*(arr[j].first-arr[i].first) == (arr[j].second-arr[i].second)*(arr[k].first-arr[i].first)){
                    cnt++;
                }
            }
            ans-=(pw[cnt]-MOD);
            ans%=MOD;
        }
    }
    cout<<ans<<endl;
    
}
```