#include<bits/stdc++.h>
#define ha 998244353
using namespace std;

struct Point
{
	int x,y;
	Point(int a=0,int b=0):x(a),y(b){}
	friend Point operator - (const Point &a,const Point &b){return Point(a.x-b.x,a.y-b.y);}
	friend int operator * (const Point &a,const Point &b){return a.x*b.y-a.y*b.x;}
} p[210];
int pw2[210];

int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d%d",&p[i].x,&p[i].y);
	pw2[0]=1;
	for(int i=1;i<=n;i++)
		pw2[i]=(pw2[i-1]<<1)%ha;
	int ans=(pw2[n]-n*(n-1)/2-n-1+ha)%ha;
	for(int i=2;i<n;i++)
		for(int j=i+1;j<=n;j++)
		{
			int sum=0;
			for(int k=1;k<i;k++)
				sum+=((p[k]-p[i])*(p[j]-p[i])==0);
			ans=(ans-pw2[sum]+1+ha)%ha;
		}
	printf("%d\n",ans);
	return 0;
}
### Prompt

Develop a solution in cpp 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>
#define ha 998244353
using namespace std;

struct Point
{
	int x,y;
	Point(int a=0,int b=0):x(a),y(b){}
	friend Point operator - (const Point &a,const Point &b){return Point(a.x-b.x,a.y-b.y);}
	friend int operator * (const Point &a,const Point &b){return a.x*b.y-a.y*b.x;}
} p[210];
int pw2[210];

int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d%d",&p[i].x,&p[i].y);
	pw2[0]=1;
	for(int i=1;i<=n;i++)
		pw2[i]=(pw2[i-1]<<1)%ha;
	int ans=(pw2[n]-n*(n-1)/2-n-1+ha)%ha;
	for(int i=2;i<n;i++)
		for(int j=i+1;j<=n;j++)
		{
			int sum=0;
			for(int k=1;k<i;k++)
				sum+=((p[k]-p[i])*(p[j]-p[i])==0);
			ans=(ans-pw2[sum]+1+ha)%ha;
		}
	printf("%d\n",ans);
	return 0;
}
```