#include<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<queue>
#include<bitset>
#include<map>
using namespace std;
template<typename __T>
inline void read(__T &x)
{
    x=0;
    int f=1;char c=getchar();
    while(!isdigit(c)){if(c=='-')	f=-1;c=getchar();}
    while(isdigit(c))	{x=x*10+c-'0';c=getchar();}
    x*=f;
}
const int mod=998244353;
int n;
int x[205],y[205];
long long pow2[205];
int main()
{
	read(n);
	for(int i=1;i<=n;i++)
	{
		read(x[i]);
		read(y[i]);
	}
	pow2[0]=1;
	for(int i=1;i<=n;i++)
		pow2[i]=pow2[i-1]*2%mod;
	long long ans=(pow2[n]-1-n+mod)%mod;
	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((y[k]-y[j])*(x[j]-x[i])==(y[j]-y[i])*(x[k]-x[j]))
					cnt++;
			ans=(ans+mod-pow2[cnt])%mod;
		}
	cout<<ans<<endl;
	return 0;
}

### Prompt

Please formulate 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<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<queue>
#include<bitset>
#include<map>
using namespace std;
template<typename __T>
inline void read(__T &x)
{
    x=0;
    int f=1;char c=getchar();
    while(!isdigit(c)){if(c=='-')	f=-1;c=getchar();}
    while(isdigit(c))	{x=x*10+c-'0';c=getchar();}
    x*=f;
}
const int mod=998244353;
int n;
int x[205],y[205];
long long pow2[205];
int main()
{
	read(n);
	for(int i=1;i<=n;i++)
	{
		read(x[i]);
		read(y[i]);
	}
	pow2[0]=1;
	for(int i=1;i<=n;i++)
		pow2[i]=pow2[i-1]*2%mod;
	long long ans=(pow2[n]-1-n+mod)%mod;
	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((y[k]-y[j])*(x[j]-x[i])==(y[j]-y[i])*(x[k]-x[j]))
					cnt++;
			ans=(ans+mod-pow2[cnt])%mod;
		}
	cout<<ans<<endl;
	return 0;
}

```