#include<bits/stdc++.h>
#define rep(i,x,y) for (int i=(x); i<=(y); i++)
#define ll long long
#define ld long double
#define inf 1000000000
using namespace std;
#define N 205
#define mod 998244353
int n,pw[N],ans;
struct node{ int x,y; }a[N];
int main(){
	scanf("%d",&n);
	pw[0]=1; rep (i,1,n) pw[i]=2ll*pw[i-1]%mod;
	ans=(pw[n]+mod-1-n)%mod;
	rep (i,1,n) scanf("%d%d",&a[i].x,&a[i].y);
	rep (i,1,n) rep (j,i+1,n){
		int sum=0;
		rep (k,j+1,n)
			if ((a[i].y-a[j].y)*(a[j].x-a[k].x)==(a[i].x-a[j].x)*(a[j].y-a[k].y)) sum++;
		ans=(ans+mod-pw[sum])%mod;
	}
	cout<<ans<<endl;
	return 0;
}
### Prompt

Please provide a CPP coded solution 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<bits/stdc++.h>
#define rep(i,x,y) for (int i=(x); i<=(y); i++)
#define ll long long
#define ld long double
#define inf 1000000000
using namespace std;
#define N 205
#define mod 998244353
int n,pw[N],ans;
struct node{ int x,y; }a[N];
int main(){
	scanf("%d",&n);
	pw[0]=1; rep (i,1,n) pw[i]=2ll*pw[i-1]%mod;
	ans=(pw[n]+mod-1-n)%mod;
	rep (i,1,n) scanf("%d%d",&a[i].x,&a[i].y);
	rep (i,1,n) rep (j,i+1,n){
		int sum=0;
		rep (k,j+1,n)
			if ((a[i].y-a[j].y)*(a[j].x-a[k].x)==(a[i].x-a[j].x)*(a[j].y-a[k].y)) sum++;
		ans=(ans+mod-pw[sum])%mod;
	}
	cout<<ans<<endl;
	return 0;
}
```