#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
using namespace std;
const int mod=998244353;
struct point{int x,y;}p[210];
bool vis[210][210];
int multi(point p1,point p2,point p0)
{
	int x1=p1.x-p0.x,y1=p1.y-p0.y;
	int x2=p2.x-p0.x,y2=p2.y-p0.y;
	return x1*y2-x2*y1;
}
int n,bin[210],sta[210],top=0;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d %d",&p[i].x,&p[i].y);
	bin[0]=1;for(int i=1;i<=n;i++) bin[i]=(bin[i-1]*2)%mod;
	int ans=(bin[n]-n-1)%mod;
	memset(vis,false,sizeof(vis));
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++)
		{
			if(i==j||vis[i][j]) continue;
			top=0;sta[++top]=i;sta[++top]=j;
			for(int k=1;k<=n;k++)
				if(i!=k&&j!=k&&multi(p[i],p[j],p[k])==0) sta[++top]=k;
			for(int k=1;k<=top;k++) for(int u=1;u<=top;u++) vis[sta[k]][sta[u]]=true;
			(ans-=(bin[top]-(top+1)))%=mod;
			//printf("ans:%d %d\n",ans,top);
			//for(int k=1;k<=top;k++) printf("%d ",sta[k]);printf("\n");
		}
	//(ans-=1)%=mod;
	printf("%d",(ans+mod)%mod);
}
### Prompt

Please formulate 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<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
using namespace std;
const int mod=998244353;
struct point{int x,y;}p[210];
bool vis[210][210];
int multi(point p1,point p2,point p0)
{
	int x1=p1.x-p0.x,y1=p1.y-p0.y;
	int x2=p2.x-p0.x,y2=p2.y-p0.y;
	return x1*y2-x2*y1;
}
int n,bin[210],sta[210],top=0;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d %d",&p[i].x,&p[i].y);
	bin[0]=1;for(int i=1;i<=n;i++) bin[i]=(bin[i-1]*2)%mod;
	int ans=(bin[n]-n-1)%mod;
	memset(vis,false,sizeof(vis));
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++)
		{
			if(i==j||vis[i][j]) continue;
			top=0;sta[++top]=i;sta[++top]=j;
			for(int k=1;k<=n;k++)
				if(i!=k&&j!=k&&multi(p[i],p[j],p[k])==0) sta[++top]=k;
			for(int k=1;k<=top;k++) for(int u=1;u<=top;u++) vis[sta[k]][sta[u]]=true;
			(ans-=(bin[top]-(top+1)))%=mod;
			//printf("ans:%d %d\n",ans,top);
			//for(int k=1;k<=top;k++) printf("%d ",sta[k]);printf("\n");
		}
	//(ans-=1)%=mod;
	printf("%d",(ans+mod)%mod);
}
```