#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod=998244353;
struct point{
	int x,y;
	point(){};
}p[210];

int n;
ll pw[210],ans;
point operator - (point a,point b){
	point ret;
	ret.x=a.x-b.x;
	ret.y=a.y-b.y;
	return ret;
}
ll cross(point a,point b){
	return a.x*b.y-a.y*b.x;
}
ll cross(point a,point b,point c){
	return abs(cross(a-c,b-c));
}
void solve(){
	cin>>n;pw[0]=1;
	for(int i=1;i<=n;++i){
		cin>>p[i].x>>p[i].y;
		pw[i]=pw[i-1]*2%mod;
	}
	ans=pw[n]-1-n;
	for(int i=1;i<=n;++i)
		for(int j=i+1;j<=n;++j){
			int cnt=0;
			for(int k=j+1;k<=n;++k)if(cross(p[i],p[j],p[k])<=0)++cnt;
			(ans+=mod-pw[cnt])%=mod;
		}
	printf("%lld\n",ans);
}
int main(){
	solve();
	
	return 0;
} 
### Prompt

Please provide a Cpp coded solution to the problem described below:

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>
using namespace std;
typedef long long ll;
const int mod=998244353;
struct point{
	int x,y;
	point(){};
}p[210];

int n;
ll pw[210],ans;
point operator - (point a,point b){
	point ret;
	ret.x=a.x-b.x;
	ret.y=a.y-b.y;
	return ret;
}
ll cross(point a,point b){
	return a.x*b.y-a.y*b.x;
}
ll cross(point a,point b,point c){
	return abs(cross(a-c,b-c));
}
void solve(){
	cin>>n;pw[0]=1;
	for(int i=1;i<=n;++i){
		cin>>p[i].x>>p[i].y;
		pw[i]=pw[i-1]*2%mod;
	}
	ans=pw[n]-1-n;
	for(int i=1;i<=n;++i)
		for(int j=i+1;j<=n;++j){
			int cnt=0;
			for(int k=j+1;k<=n;++k)if(cross(p[i],p[j],p[k])<=0)++cnt;
			(ans+=mod-pw[cnt])%=mod;
		}
	printf("%lld\n",ans);
}
int main(){
	solve();
	
	return 0;
} 
```