#include <stdio.h>
#include <string.h>
#define R register
#define MN 205
#define P 998244353
int n,x[MN],y[MN],p[MN],ans;
inline int read(){
	R int x; R bool f; R char c;
	for (f=0; (c=getchar())<'0'||c>'9'; f=c=='-');
	for (x=c^'0'; (c=getchar())>='0'&&c<='9'; x=(x<<1)+(x<<3)+(c^'0'));
	return f?-x:x;
}
inline void del(int &x,int y){x-=y; if (x<0) x+=P;}
int main(){
	n=read();for (R int i=1; i<=n; ++i) x[i]=read(),y[i]=read();
	p[0]=1;for (R int i=1; i<=n; ++i) p[i]=p[i-1]<<1,p[i]>=P?p[i]-=P:0;
	ans=p[n];del(ans,n+1);	
	for (R int i=2; i<=n; ++i)
		for (R int j=1,cnt; j<i; ++j){
			cnt=0;
			for (R int k=1; k<j; ++k)
				if ((x[k]-x[i])*(y[j]-y[i])==(y[k]-y[i])*(x[j]-x[i])) ++cnt;
			del(ans,p[cnt]);	
		}printf("%d\n",ans);
}
### 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 <stdio.h>
#include <string.h>
#define R register
#define MN 205
#define P 998244353
int n,x[MN],y[MN],p[MN],ans;
inline int read(){
	R int x; R bool f; R char c;
	for (f=0; (c=getchar())<'0'||c>'9'; f=c=='-');
	for (x=c^'0'; (c=getchar())>='0'&&c<='9'; x=(x<<1)+(x<<3)+(c^'0'));
	return f?-x:x;
}
inline void del(int &x,int y){x-=y; if (x<0) x+=P;}
int main(){
	n=read();for (R int i=1; i<=n; ++i) x[i]=read(),y[i]=read();
	p[0]=1;for (R int i=1; i<=n; ++i) p[i]=p[i-1]<<1,p[i]>=P?p[i]-=P:0;
	ans=p[n];del(ans,n+1);	
	for (R int i=2; i<=n; ++i)
		for (R int j=1,cnt; j<i; ++j){
			cnt=0;
			for (R int k=1; k<j; ++k)
				if ((x[k]-x[i])*(y[j]-y[i])==(y[k]-y[i])*(x[j]-x[i])) ++cnt;
			del(ans,p[cnt]);	
		}printf("%d\n",ans);
}
```