#include<cstdio>
#include<algorithm>
const int mod=998244353;
int N,pw2[210];
struct Point{int x,y;}P[210];
int o,L[210];
bool cmp(int i,int j){
	int ti=P[i].y<P[o].y||P[i].y==P[o].y&&P[i].x<P[o].x,
		tj=P[j].y<P[o].y||P[j].y==P[o].y&&P[j].x<P[o].x;
	if(ti!=tj)return ti<tj;
	return(P[i].x-P[o].x)*(P[j].y-P[o].y)>(P[i].y-P[o].y)*(P[j].x-P[o].x);
}
int main(){
	scanf("%d",&N);
	for(int i=0;i<N;i++)scanf("%d%d",&P[i].x,&P[i].y);
	for(int i=*pw2=1;i<=N;i++)pw2[i]=pw2[i-1]*2%mod;
	int s=0;
	for(o=0;o<N;o++){
		int m=0;
		for(int i=0;i<N;i++)if(i!=o)L[m++]=i;
		std::sort(L,L+m,cmp);
		for(int i=0,t=0;i<m;i++){
			if(i&&cmp(L[i-1],L[i]))t=0;
			(s+=pw2[t++])%=mod;
		}
	}
	s=(s*(mod+1ll)/2+N+1)%mod;
	printf("%d\n",(pw2[N]+mod-s)%mod);
}
### Prompt

Your task is to create 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<algorithm>
const int mod=998244353;
int N,pw2[210];
struct Point{int x,y;}P[210];
int o,L[210];
bool cmp(int i,int j){
	int ti=P[i].y<P[o].y||P[i].y==P[o].y&&P[i].x<P[o].x,
		tj=P[j].y<P[o].y||P[j].y==P[o].y&&P[j].x<P[o].x;
	if(ti!=tj)return ti<tj;
	return(P[i].x-P[o].x)*(P[j].y-P[o].y)>(P[i].y-P[o].y)*(P[j].x-P[o].x);
}
int main(){
	scanf("%d",&N);
	for(int i=0;i<N;i++)scanf("%d%d",&P[i].x,&P[i].y);
	for(int i=*pw2=1;i<=N;i++)pw2[i]=pw2[i-1]*2%mod;
	int s=0;
	for(o=0;o<N;o++){
		int m=0;
		for(int i=0;i<N;i++)if(i!=o)L[m++]=i;
		std::sort(L,L+m,cmp);
		for(int i=0,t=0;i<m;i++){
			if(i&&cmp(L[i-1],L[i]))t=0;
			(s+=pw2[t++])%=mod;
		}
	}
	s=(s*(mod+1ll)/2+N+1)%mod;
	printf("%d\n",(pw2[N]+mod-s)%mod);
}
```