#include<bits/stdc++.h>
using namespace std;
const long long mod = 998244353;
struct node{
	int x;
	int y;
}no[205];
long long Qpow(long long x,int n)
{
	long long ans=1;
	while(n)
	{
		if(n&1)
			ans=(ans*x)%mod;
		x=(x*x)%mod;
		n=n>>1;
	}
	return ans;
}
int main()
{
	int n;
	scanf("%d",&n);
	long long ans=Qpow(2,n)-1-n;
	for(int i=0;i<n;i++)
		scanf("%d%d",&no[i].x,&no[i].y);
	for(int i=0;i<n;i++)
	{
		for(int j=i+1;j<n;j++)
		{
			int sum=0;
			for(int k=j+1;k<n;k++)
				if ((no[j].x-no[i].x) * (no[k].y-no[j].y) == (no[k].x-no[j].x) * (no[j].y-no[i].y)) 
					sum++;
			ans=(ans-Qpow(2,sum)+mod)%mod;
		}	
	}	
	printf("%lld\n",ans%mod); 
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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;
const long long mod = 998244353;
struct node{
	int x;
	int y;
}no[205];
long long Qpow(long long x,int n)
{
	long long ans=1;
	while(n)
	{
		if(n&1)
			ans=(ans*x)%mod;
		x=(x*x)%mod;
		n=n>>1;
	}
	return ans;
}
int main()
{
	int n;
	scanf("%d",&n);
	long long ans=Qpow(2,n)-1-n;
	for(int i=0;i<n;i++)
		scanf("%d%d",&no[i].x,&no[i].y);
	for(int i=0;i<n;i++)
	{
		for(int j=i+1;j<n;j++)
		{
			int sum=0;
			for(int k=j+1;k<n;k++)
				if ((no[j].x-no[i].x) * (no[k].y-no[j].y) == (no[k].x-no[j].x) * (no[j].y-no[i].y)) 
					sum++;
			ans=(ans-Qpow(2,sum)+mod)%mod;
		}	
	}	
	printf("%lld\n",ans%mod); 
	return 0;
}
```