#include<iostream>
#include<cstdio>
using namespace std;
int vis[210][210]; 
int area(pair<int,int>a,pair<int,int>b,pair<int,int>c)
{
	return a.first*b.second+b.first*c.second+c.first*a.second-a.second*b.first-b.second*c.first-c.second*a.first;
}
int n;
int ans;
pair<int,int>co[210];
int pw[210];
const int md=998244353;
int add(int x,int y)
{
	x+=y;
	if(x>=md)x-=md;
	return x;
}
int main()
{
	scanf("%d",&n);
	pw[0]=1;
	for(int i=1;i<=n;i++)pw[i]=add(pw[i-1],pw[i-1]);
	for(int i=1;i<=n;i++)scanf("%d%d",&co[i].first,&co[i].second);
	ans=pw[n]-1;
	for(int i=1;i<=n;i++)
	{
		ans--;
		if(ans<0)ans+=md;
		for(int j=i+1;j<=n;j++)
		{
			if(vis[i][j])continue;
			int cnt=1;
			for(int k=j+1;k<=n;k++)
			{
				if(area(co[i],co[j],co[k]))continue;
				cnt++;
				vis[i][k]=true;
			}
			ans-=pw[cnt]-1;
			if(ans<0)ans+=md; 
		}
	} 
	printf("%d",ans);
	return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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<cstdio>
using namespace std;
int vis[210][210]; 
int area(pair<int,int>a,pair<int,int>b,pair<int,int>c)
{
	return a.first*b.second+b.first*c.second+c.first*a.second-a.second*b.first-b.second*c.first-c.second*a.first;
}
int n;
int ans;
pair<int,int>co[210];
int pw[210];
const int md=998244353;
int add(int x,int y)
{
	x+=y;
	if(x>=md)x-=md;
	return x;
}
int main()
{
	scanf("%d",&n);
	pw[0]=1;
	for(int i=1;i<=n;i++)pw[i]=add(pw[i-1],pw[i-1]);
	for(int i=1;i<=n;i++)scanf("%d%d",&co[i].first,&co[i].second);
	ans=pw[n]-1;
	for(int i=1;i<=n;i++)
	{
		ans--;
		if(ans<0)ans+=md;
		for(int j=i+1;j<=n;j++)
		{
			if(vis[i][j])continue;
			int cnt=1;
			for(int k=j+1;k<=n;k++)
			{
				if(area(co[i],co[j],co[k]))continue;
				cnt++;
				vis[i][k]=true;
			}
			ans-=pw[cnt]-1;
			if(ans<0)ans+=md; 
		}
	} 
	printf("%d",ans);
	return 0;
}
```