#include <bits/stdc++.h>
#define rep(i,n)for(int i=0;i<(n);i++)
#define MOD 998244353
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

ll ppow(ll a,ll b){
	ll res=1;
	while(b){
		if(b&1)res=(res*a)%MOD;
		a=(a*a)%MOD;
		b>>=1;
	}
	return res;
}
struct Point{int x,y;};
int cross(Point a,Point b){
	return a.x*b.y-a.y*b.x;
}
Point operator-(Point a,Point b){
	return {a.x-b.x,a.y-b.y};
}

Point p[300];
int main(){
	int n;cin>>n;
	rep(i,n){
		scanf("%d%d",&p[i].x,&p[i].y);
	}
	sort(p,p+n,[](Point a,Point b){
		if(a.x==b.x)return a.y<b.y;
		return a.x<b.x;
	});
	int ans=(ppow(2,n)+MOD-(1+n)%MOD)%MOD;
	rep(i,n){
		for(int j=i+1;j<n;j++){
			Point pp=p[j]-p[i];
			bool ok=true;
			int cnt=2;
			rep(k,n){
				if(k==i||k==j)continue;
				if(cross(pp,p[k]-p[j])==0){
					if(k<j){ok=false;break;}
					else cnt++;
				}
			}
			if(ok){
				ans=(ans+MOD-(ppow(2,cnt)+MOD-(1+cnt)%MOD)%MOD)%MOD;
			}
		}
	}
	cout<<ans<<endl;
}
### Prompt

Your challenge is to write 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 rep(i,n)for(int i=0;i<(n);i++)
#define MOD 998244353
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

ll ppow(ll a,ll b){
	ll res=1;
	while(b){
		if(b&1)res=(res*a)%MOD;
		a=(a*a)%MOD;
		b>>=1;
	}
	return res;
}
struct Point{int x,y;};
int cross(Point a,Point b){
	return a.x*b.y-a.y*b.x;
}
Point operator-(Point a,Point b){
	return {a.x-b.x,a.y-b.y};
}

Point p[300];
int main(){
	int n;cin>>n;
	rep(i,n){
		scanf("%d%d",&p[i].x,&p[i].y);
	}
	sort(p,p+n,[](Point a,Point b){
		if(a.x==b.x)return a.y<b.y;
		return a.x<b.x;
	});
	int ans=(ppow(2,n)+MOD-(1+n)%MOD)%MOD;
	rep(i,n){
		for(int j=i+1;j<n;j++){
			Point pp=p[j]-p[i];
			bool ok=true;
			int cnt=2;
			rep(k,n){
				if(k==i||k==j)continue;
				if(cross(pp,p[k]-p[j])==0){
					if(k<j){ok=false;break;}
					else cnt++;
				}
			}
			if(ok){
				ans=(ans+MOD-(ppow(2,cnt)+MOD-(1+cnt)%MOD)%MOD)%MOD;
			}
		}
	}
	cout<<ans<<endl;
}
```