#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;

const int N=205;
const int MOD=998244353;

int n,bin[N],b[N];
bool vis[N][N];
struct data{int x,y;}a[N];

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*10+ch-'0';ch=getchar();}
	return x*f;
}

int cross(int k,int i,int j)
{
	return (a[i].x-a[k].x)*(a[j].y-a[k].y)-(a[i].y-a[k].y)*(a[j].x-a[k].x);
}

int main()
{
	n=read();
	bin[0]=1;
	for (int i=1;i<=n;i++) bin[i]=bin[i-1]*2%MOD;
	for (int i=1;i<=n;i++) a[i].x=read(),a[i].y=read();
	int ans=bin[n];
	for (int i=1;i<n;i++)
		for (int j=i+1;j<=n;j++)
			if (!vis[i][j])
			{
				int tot=0;
				b[++tot]=i;b[++tot]=j;
				for (int k=j+1;k<=n;k++) if (!cross(i,j,k)) b[++tot]=k;
				for (int k=1;k<tot;k++)
					for (int l=k+1;l<=tot;l++)
						vis[b[k]][b[l]]=1;
				(ans-=bin[tot]-tot-1)%=MOD;
			}
	(ans-=n+1)%=MOD;
	ans+=ans<0?MOD:0;
	printf("%d",ans);
	return 0;
}
### 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<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;

const int N=205;
const int MOD=998244353;

int n,bin[N],b[N];
bool vis[N][N];
struct data{int x,y;}a[N];

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*10+ch-'0';ch=getchar();}
	return x*f;
}

int cross(int k,int i,int j)
{
	return (a[i].x-a[k].x)*(a[j].y-a[k].y)-(a[i].y-a[k].y)*(a[j].x-a[k].x);
}

int main()
{
	n=read();
	bin[0]=1;
	for (int i=1;i<=n;i++) bin[i]=bin[i-1]*2%MOD;
	for (int i=1;i<=n;i++) a[i].x=read(),a[i].y=read();
	int ans=bin[n];
	for (int i=1;i<n;i++)
		for (int j=i+1;j<=n;j++)
			if (!vis[i][j])
			{
				int tot=0;
				b[++tot]=i;b[++tot]=j;
				for (int k=j+1;k<=n;k++) if (!cross(i,j,k)) b[++tot]=k;
				for (int k=1;k<tot;k++)
					for (int l=k+1;l<=tot;l++)
						vis[b[k]][b[l]]=1;
				(ans-=bin[tot]-tot-1)%=MOD;
			}
	(ans-=n+1)%=MOD;
	ans+=ans<0?MOD:0;
	printf("%d",ans);
	return 0;
}
```