/* --- author: dxm --- */
#include<bits/stdc++.h>
using namespace std;

#define INF 1e9
#define Inf 1e18
#define rep(i,n) for(int (i)=0;(i)<n;i++)
#define REP(i,n) for(int (i)=1;(i)<=n;i++)
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
#define fst first
#define snd second
typedef long long ll;
typedef double db;
typedef long double ldb;
typedef unsigned int uint;
typedef unsigned long long ull;
#define DEBUG

const int maxn=205;
const int mod=998244353;
int ans,n;
int x[maxn],y[maxn],t2[maxn];

bool coli(int i,int j,int k){return (y[j]-y[i])*(x[k]-x[j])==(y[k]-y[j])*(x[j]-x[i]);}

int main(){
#ifndef DEBUG
	freopen("my.in","r",stdin);
	freopen("my.out","w",stdout);
#endif
	scanf("%d",&n);
	t2[0]=1;
	REP(i,n)t2[i]=2LL*t2[i-1]%mod;
	ans=(t2[n]-n-1)%mod;
	if(ans<0)ans+=mod;
	rep(i,n)scanf("%d%d",&x[i],&y[i]);
	rep(i,n)for(int j=i+1;j<n;j++){
		int cnt=0;
		for(int k=j+1;k<n;k++)if(coli(i,j,k))cnt++;
		ans-=t2[cnt];
		if(ans<0)ans+=mod;
	}
	printf("%d",ans);
	return 0;
}

/*
Input:
-----------------
Output:
*/
### Prompt

Generate 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
/* --- author: dxm --- */
#include<bits/stdc++.h>
using namespace std;

#define INF 1e9
#define Inf 1e18
#define rep(i,n) for(int (i)=0;(i)<n;i++)
#define REP(i,n) for(int (i)=1;(i)<=n;i++)
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
#define fst first
#define snd second
typedef long long ll;
typedef double db;
typedef long double ldb;
typedef unsigned int uint;
typedef unsigned long long ull;
#define DEBUG

const int maxn=205;
const int mod=998244353;
int ans,n;
int x[maxn],y[maxn],t2[maxn];

bool coli(int i,int j,int k){return (y[j]-y[i])*(x[k]-x[j])==(y[k]-y[j])*(x[j]-x[i]);}

int main(){
#ifndef DEBUG
	freopen("my.in","r",stdin);
	freopen("my.out","w",stdout);
#endif
	scanf("%d",&n);
	t2[0]=1;
	REP(i,n)t2[i]=2LL*t2[i-1]%mod;
	ans=(t2[n]-n-1)%mod;
	if(ans<0)ans+=mod;
	rep(i,n)scanf("%d%d",&x[i],&y[i]);
	rep(i,n)for(int j=i+1;j<n;j++){
		int cnt=0;
		for(int k=j+1;k<n;k++)if(coli(i,j,k))cnt++;
		ans-=t2[cnt];
		if(ans<0)ans+=mod;
	}
	printf("%d",ans);
	return 0;
}

/*
Input:
-----------------
Output:
*/
```