#include<bits/stdc++.h>
#define L long long
#define pb push_back
#define pi pair<int,int>
#define pii pair<pair<int,int>,int>
#define aa first
#define bb second
#define mp make_pair
#define mpp(a,b,c) mp(mp(a,b),c)
using namespace std;
int n,x[210],y[210],p;
const int q=998244353;
inline int power(int a,int b)
{
	if(!b)
	  return 1;
	int c=power(a,b>>1);
	c=(L)c*c%q;
	if(b&1)
	  c=(L)c*a%q;
	return c;
}
inline bool chk(int i,int j,int k)
{
	return (x[i]-x[k])*(y[j]-y[k])-(x[j]-x[k])*(y[i]-y[k])==0;
}
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i,j,k,l,u;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
	  scanf("%d%d",&x[i],&y[i]);
	p=power(2,n)-1-n;
	for(i=1;i<=n;i++)
	  for(j=i+1;j<=n;j++)
	    {
	     for(k=1,l=4,u=3;k<=n;k++)
	       if(k!=i && k!=j && chk(i,j,k))
	         if(k<j)
	           {
				l=u=0;
				break;
			   }
			 else
			   {
			    l=(l<<1)%q;
			    u++;
			   }
		 p=(p-l+u)%q;
		}
	p=(p+q)%q;
	printf("%d\n",p);
	return 0;
}

### 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<bits/stdc++.h>
#define L long long
#define pb push_back
#define pi pair<int,int>
#define pii pair<pair<int,int>,int>
#define aa first
#define bb second
#define mp make_pair
#define mpp(a,b,c) mp(mp(a,b),c)
using namespace std;
int n,x[210],y[210],p;
const int q=998244353;
inline int power(int a,int b)
{
	if(!b)
	  return 1;
	int c=power(a,b>>1);
	c=(L)c*c%q;
	if(b&1)
	  c=(L)c*a%q;
	return c;
}
inline bool chk(int i,int j,int k)
{
	return (x[i]-x[k])*(y[j]-y[k])-(x[j]-x[k])*(y[i]-y[k])==0;
}
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i,j,k,l,u;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
	  scanf("%d%d",&x[i],&y[i]);
	p=power(2,n)-1-n;
	for(i=1;i<=n;i++)
	  for(j=i+1;j<=n;j++)
	    {
	     for(k=1,l=4,u=3;k<=n;k++)
	       if(k!=i && k!=j && chk(i,j,k))
	         if(k<j)
	           {
				l=u=0;
				break;
			   }
			 else
			   {
			    l=(l<<1)%q;
			    u++;
			   }
		 p=(p-l+u)%q;
		}
	p=(p+q)%q;
	printf("%d\n",p);
	return 0;
}

```