#include<bits/stdc++.h>
using namespace std;
inline int read(){
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+ch-'0';ch=getchar();}
	return x*f;
}
#define MN 200
#define mod 998244353
int n,x[MN+5],y[MN+5];
int b[MN+5][MN+5],ans,pw[MN+5],q[MN+5],top;
int main(){
	n=read();pw[0]=1;register int i,j,l,r,k;
    for(j=1;j<=n;++j) pw[j]=2*pw[j-1]%mod;ans=(pw[n]-n-1+mod)%mod;
    for(i=1;i<=n;++i) x[i]=read(),y[i]=read();
    for(i=1;i<=n;++i) for(j=i+1;j<=n;++j) if(!b[i][j]){
        q[top=1]=i;q[top=2]=j;
        for(k=j+1;k<=n;++k) if((x[j]-x[i])*(y[k]-y[i])==(x[k]-x[i])*(y[j]-y[i])) q[++top]=k;
        for(l=1;l<top;++l) for(r=l+1;r<=top;++r) b[q[l]][q[r]]=1;
        ans=((ans-pw[top]+top+1)%mod+mod)%mod;
    }
    cout<<ans;
    return 0;
}
### Prompt

Your task is to create 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;
inline int read(){
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+ch-'0';ch=getchar();}
	return x*f;
}
#define MN 200
#define mod 998244353
int n,x[MN+5],y[MN+5];
int b[MN+5][MN+5],ans,pw[MN+5],q[MN+5],top;
int main(){
	n=read();pw[0]=1;register int i,j,l,r,k;
    for(j=1;j<=n;++j) pw[j]=2*pw[j-1]%mod;ans=(pw[n]-n-1+mod)%mod;
    for(i=1;i<=n;++i) x[i]=read(),y[i]=read();
    for(i=1;i<=n;++i) for(j=i+1;j<=n;++j) if(!b[i][j]){
        q[top=1]=i;q[top=2]=j;
        for(k=j+1;k<=n;++k) if((x[j]-x[i])*(y[k]-y[i])==(x[k]-x[i])*(y[j]-y[i])) q[++top]=k;
        for(l=1;l<top;++l) for(r=l+1;r<=top;++r) b[q[l]][q[r]]=1;
        ans=((ans-pw[top]+top+1)%mod+mod)%mod;
    }
    cout<<ans;
    return 0;
}
```