#include <complex>
#include <vector>
#include <set>
#include <cstdio>
using namespace std;
 
const double EPS = 1e-12;
typedef complex<long double> P;

struct L : public vector<P> {
  L(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};
bool intersectSP(const L &s, const P &p) {
  return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS; // triangle inequality
}
 
long long pow_binary_mod(long long x,long long y,long long M){
	long long z=1;
	for(;y;y>>=1){
		if((y&1)!=0)z=z*x%M;
		x=x*x%M;
	}
	return z;
}
 
int main(){
	int M=998244353;
	int N,x,y;
	scanf("%d",&N);
	vector<P>v(N);
	int r=pow_binary_mod(2,N,M);
	set<L>se;
	for(int i=0;i<N;i++)scanf("%d%d",&x,&y),v[i]={(double)x,(double)y};
	for(int i=0;i<N;i++)for(int j=i+1;j<N;j++){
		L l(v[i],v[j]);
		int n=0;
		for(int k=0;k<N;k++)if(k!=i&&k!=j&&intersectSP(l,v[k]))n++;
		r=(r-pow_binary_mod(2,n,M))%M;
	}
	printf("%d\n",((r-N-1)%M+M)%M);
}
### 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 <complex>
#include <vector>
#include <set>
#include <cstdio>
using namespace std;
 
const double EPS = 1e-12;
typedef complex<long double> P;

struct L : public vector<P> {
  L(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};
bool intersectSP(const L &s, const P &p) {
  return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS; // triangle inequality
}
 
long long pow_binary_mod(long long x,long long y,long long M){
	long long z=1;
	for(;y;y>>=1){
		if((y&1)!=0)z=z*x%M;
		x=x*x%M;
	}
	return z;
}
 
int main(){
	int M=998244353;
	int N,x,y;
	scanf("%d",&N);
	vector<P>v(N);
	int r=pow_binary_mod(2,N,M);
	set<L>se;
	for(int i=0;i<N;i++)scanf("%d%d",&x,&y),v[i]={(double)x,(double)y};
	for(int i=0;i<N;i++)for(int j=i+1;j<N;j++){
		L l(v[i],v[j]);
		int n=0;
		for(int k=0;k<N;k++)if(k!=i&&k!=j&&intersectSP(l,v[k]))n++;
		r=(r-pow_binary_mod(2,n,M))%M;
	}
	printf("%d\n",((r-N-1)%M+M)%M);
}
```