#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mod 998244353
#define N 210

int n;

ll power(ll x,ll y) {
	if (!y) return 1;
	ll ret=power(x,y>>1)%mod;
	ret=ret*ret%mod;
	if (y&1) ret=ret*x%mod;
	return ret%mod;
}

int x[N],y[N],A,B,cnt;
ll ans,C;

int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d%d",&x[i],&y[i]);
	ans=power(2,n);
	ans=(ans-1+mod)%mod;
	ans=(ans-n+mod)%mod;
	ans=(ans-(ll)(n-1)*n/2+mod)%mod;
	
	for (int i=1;i<=n;i++)
		for (int j=i+1;j<=n;j++)
		{
			A=y[i]-y[j];
			B=x[j]-x[i];
			C=-x[i]*A-y[i]*B;
			cnt=2;
			for (int k=1;k<=n;k++)
			{
				if (k==i || k==j) continue;
				if (A*x[k]+B*y[k]+C!=0) continue;
				if (k<j) break;
				cnt++;
			}
			ans=(ans-power(2,cnt)+mod)%mod;
			ans=(ans+1)%mod;
			ans=(ans+cnt)%mod;
			ans=(ans+(ll)(cnt-1)*cnt/2)%mod;
		}
	printf("%lld\n",ans);
	return 0;
}
### Prompt

Please create a solution in Cpp 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 <bits/stdc++.h>
using namespace std;
#define ll long long
#define mod 998244353
#define N 210

int n;

ll power(ll x,ll y) {
	if (!y) return 1;
	ll ret=power(x,y>>1)%mod;
	ret=ret*ret%mod;
	if (y&1) ret=ret*x%mod;
	return ret%mod;
}

int x[N],y[N],A,B,cnt;
ll ans,C;

int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d%d",&x[i],&y[i]);
	ans=power(2,n);
	ans=(ans-1+mod)%mod;
	ans=(ans-n+mod)%mod;
	ans=(ans-(ll)(n-1)*n/2+mod)%mod;
	
	for (int i=1;i<=n;i++)
		for (int j=i+1;j<=n;j++)
		{
			A=y[i]-y[j];
			B=x[j]-x[i];
			C=-x[i]*A-y[i]*B;
			cnt=2;
			for (int k=1;k<=n;k++)
			{
				if (k==i || k==j) continue;
				if (A*x[k]+B*y[k]+C!=0) continue;
				if (k<j) break;
				cnt++;
			}
			ans=(ans-power(2,cnt)+mod)%mod;
			ans=(ans+1)%mod;
			ans=(ans+cnt)%mod;
			ans=(ans+(ll)(cnt-1)*cnt/2)%mod;
		}
	printf("%lld\n",ans);
	return 0;
}
```