#include <algorithm>
#include <cstdio>
const int N=205,mo=998244353;
int pw[N],s;
struct P{
	int x,y;
	P(const int xx=0,const int yy=0):x(xx),y(yy){}
}p[N];
P operator -(P a,P b){return P(a.x-b.x,a.y-b.y);}
int operator *(P a,P b){return a.x*b.y-a.y*b.x;}
bool operator <(P a,P b){return a.x!=b.x?a.x<b.x:a.y<b.y;}
bool cmp(P a,P b){return (a-p[s])*(b-p[s])<0;}
int main(){
	int n;
	scanf("%d\n",&n);
	for (int i=1;i<=n;i++) scanf("%d%d",&p[i].x,&p[i].y);
	pw[0]=1;
	for (int i=1;i<=n;i++) pw[i]=pw[i-1]*2%mo;
	int ans=pw[n]-n-1;
	for (int i=1;i<=n;i++){
		s=i;
		for (int j=i+1;j<=n;j++)
			if (p[j]<p[s]) s=j;
		std::swap(p[i],p[s]);s=i;
		std::sort(p+i+1,p+n+1,cmp);
		for (int j=i+1,k=i+1;j<=n;j=k){
			for (;k<=n && (p[j]-p[i])*(p[k]-p[i])==0;k++);
			(ans-=pw[k-j]-1)%=mo;
		}
	}
	printf("%d\n",(ans+mo)%mo);
}
### Prompt

Generate 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 <algorithm>
#include <cstdio>
const int N=205,mo=998244353;
int pw[N],s;
struct P{
	int x,y;
	P(const int xx=0,const int yy=0):x(xx),y(yy){}
}p[N];
P operator -(P a,P b){return P(a.x-b.x,a.y-b.y);}
int operator *(P a,P b){return a.x*b.y-a.y*b.x;}
bool operator <(P a,P b){return a.x!=b.x?a.x<b.x:a.y<b.y;}
bool cmp(P a,P b){return (a-p[s])*(b-p[s])<0;}
int main(){
	int n;
	scanf("%d\n",&n);
	for (int i=1;i<=n;i++) scanf("%d%d",&p[i].x,&p[i].y);
	pw[0]=1;
	for (int i=1;i<=n;i++) pw[i]=pw[i-1]*2%mo;
	int ans=pw[n]-n-1;
	for (int i=1;i<=n;i++){
		s=i;
		for (int j=i+1;j<=n;j++)
			if (p[j]<p[s]) s=j;
		std::swap(p[i],p[s]);s=i;
		std::sort(p+i+1,p+n+1,cmp);
		for (int j=i+1,k=i+1;j<=n;j=k){
			for (;k<=n && (p[j]-p[i])*(p[k]-p[i])==0;k++);
			(ans-=pw[k-j]-1)%=mo;
		}
	}
	printf("%d\n",(ans+mo)%mo);
}
```