#include<cstdio>
using namespace std;
typedef long long ll;
const int Mod=998244353;
inline char tc(void){
	static char fl[10000],*A=fl,*B=fl;
	return A==B&&(B=(A=fl)+fread(fl,1,10000,stdin),A==B)?EOF:*A++;
}
inline int read(void){
	int a=0;static char c;
	while((c=tc())<'0'||c>'9');
	while(c>='0'&&c<='9')a=a*10+c-'0',c=tc();
	return a;
}
int n,x[201],y[201],o[201],cnt;
ll ans;
int main(void){
	register int i,j,k;
	n=read();
	o[0]=1;
	for(i=1;i<=n;++i)
		x[i]=read(),y[i]=read(),(o[i]=o[i-1]<<1)%=Mod;
	ans=((o[n]-1-n-(n*(n-1)>>1))%Mod+Mod)%Mod;
	for(i=1;i<=n;++i)
		for(j=i+1;j<=n;++j){
			cnt=0;
			for(k=j+1;k<=n;++k)
				if((x[i]-x[j])*(y[i]-y[k])==(x[i]-x[k])*(y[i]-y[j]))++cnt;
			ans=(ans-o[cnt]+1+Mod)%Mod;
		}
	printf("%lld",ans);
	return 0;
}
### 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>
using namespace std;
typedef long long ll;
const int Mod=998244353;
inline char tc(void){
	static char fl[10000],*A=fl,*B=fl;
	return A==B&&(B=(A=fl)+fread(fl,1,10000,stdin),A==B)?EOF:*A++;
}
inline int read(void){
	int a=0;static char c;
	while((c=tc())<'0'||c>'9');
	while(c>='0'&&c<='9')a=a*10+c-'0',c=tc();
	return a;
}
int n,x[201],y[201],o[201],cnt;
ll ans;
int main(void){
	register int i,j,k;
	n=read();
	o[0]=1;
	for(i=1;i<=n;++i)
		x[i]=read(),y[i]=read(),(o[i]=o[i-1]<<1)%=Mod;
	ans=((o[n]-1-n-(n*(n-1)>>1))%Mod+Mod)%Mod;
	for(i=1;i<=n;++i)
		for(j=i+1;j<=n;++j){
			cnt=0;
			for(k=j+1;k<=n;++k)
				if((x[i]-x[j])*(y[i]-y[k])==(x[i]-x[k])*(y[i]-y[j]))++cnt;
			ans=(ans-o[cnt]+1+Mod)%Mod;
		}
	printf("%lld",ans);
	return 0;
}
```