#include<bits/stdc++.h>
using namespace std;

using ll=long long;
using ld=long double;
using P=complex<ld>;
const ll MOD=998244353;

ld cross(P x,P y){
    return x.real()*y.imag()-x.imag()*y.real();
}
bool onLine(P x,P y,P z){
    return cross(x-y,z-x)==0;
}
int main(){
    int n;
    cin>>n;
    vector<P> xy(n);
    for(int i=0;i<n;i++){
        ld x,y;
        cin>>x>>y;
        xy[i]={x,y};
    }
    
    ll res=1;
    for(int i=0;i<n;i++){
        res*=2;
        res%=MOD;
    }
    res--;
    for(int i=0;i<n;i++){
        vector<int> used(n,false);
        res--;
        for(int j=i+1;j<n;j++){
            if(used[j]) continue;
            ll cnt=2;
            for(int k=j+1;k<n;k++){
                if(onLine(xy[i],xy[j],xy[k])){
                    used[k]=true;
                    cnt*=2;
                    cnt%=MOD;
                }
            }
            res-=(cnt-1);
            res%=MOD;
        }
    }
    res=(res%MOD+MOD)%MOD;
    cout<<res<<endl;
    return 0;
}
### Prompt

Generate a Cpp solution 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<bits/stdc++.h>
using namespace std;

using ll=long long;
using ld=long double;
using P=complex<ld>;
const ll MOD=998244353;

ld cross(P x,P y){
    return x.real()*y.imag()-x.imag()*y.real();
}
bool onLine(P x,P y,P z){
    return cross(x-y,z-x)==0;
}
int main(){
    int n;
    cin>>n;
    vector<P> xy(n);
    for(int i=0;i<n;i++){
        ld x,y;
        cin>>x>>y;
        xy[i]={x,y};
    }
    
    ll res=1;
    for(int i=0;i<n;i++){
        res*=2;
        res%=MOD;
    }
    res--;
    for(int i=0;i<n;i++){
        vector<int> used(n,false);
        res--;
        for(int j=i+1;j<n;j++){
            if(used[j]) continue;
            ll cnt=2;
            for(int k=j+1;k<n;k++){
                if(onLine(xy[i],xy[j],xy[k])){
                    used[k]=true;
                    cnt*=2;
                    cnt%=MOD;
                }
            }
            res-=(cnt-1);
            res%=MOD;
        }
    }
    res=(res%MOD+MOD)%MOD;
    cout<<res<<endl;
    return 0;
}
```