#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int maxn=205;
ll x[maxn],y[maxn];
const ll mod=998244353;

ll power_mod(ll a,ll b){
	ll ans=1;
	a%=mod;
	while(b){
		if(b&1) ans=(ans*a)%mod;
		a=(a*a)%mod;
		b>>=1;
	}
	return ans;
}

ll gcd(ll a,ll b){
	return b==0?a:gcd(b,a%b);
}
map<pair<ll,ll>,ll>a;

int main(int argc, char const *argv[])
{
	ios::sync_with_stdio(false);
	int n;
	while(cin>>n){
		for(int i=1;i<=n;i++)
			cin>>x[i]>>y[i];
		ll ans=(power_mod(2,n)-1LL-n+mod)%mod;
		ll tmp1,tmp2,tmp;
		for(int i=1;i<=n;i++){
			a.clear();
			for(int j=i+1;j<=n;j++){
				tmp1=x[i]-x[j];
				tmp2=y[i]-y[j];
				tmp=gcd(tmp1,tmp2);
				tmp1/=tmp,tmp2/=tmp;
				a[make_pair(tmp1,tmp2)]++;
			}
			for(auto iter:a){
				ll temp=(power_mod(2,iter.second)-1+mod)%mod;
				ans=(ans-temp+mod)%mod;
			}
		}
		cout<<ans<<endl;
	}
	return 0;
}
### Prompt

Create a solution in Cpp for 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 <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int maxn=205;
ll x[maxn],y[maxn];
const ll mod=998244353;

ll power_mod(ll a,ll b){
	ll ans=1;
	a%=mod;
	while(b){
		if(b&1) ans=(ans*a)%mod;
		a=(a*a)%mod;
		b>>=1;
	}
	return ans;
}

ll gcd(ll a,ll b){
	return b==0?a:gcd(b,a%b);
}
map<pair<ll,ll>,ll>a;

int main(int argc, char const *argv[])
{
	ios::sync_with_stdio(false);
	int n;
	while(cin>>n){
		for(int i=1;i<=n;i++)
			cin>>x[i]>>y[i];
		ll ans=(power_mod(2,n)-1LL-n+mod)%mod;
		ll tmp1,tmp2,tmp;
		for(int i=1;i<=n;i++){
			a.clear();
			for(int j=i+1;j<=n;j++){
				tmp1=x[i]-x[j];
				tmp2=y[i]-y[j];
				tmp=gcd(tmp1,tmp2);
				tmp1/=tmp,tmp2/=tmp;
				a[make_pair(tmp1,tmp2)]++;
			}
			for(auto iter:a){
				ll temp=(power_mod(2,iter.second)-1+mod)%mod;
				ans=(ans-temp+mod)%mod;
			}
		}
		cout<<ans<<endl;
	}
	return 0;
}
```