#include<bits/stdc++.h>
#define ll long long
#define mod 998244353
#define eps 1e-10
#define N 209
using namespace std;

int n,cnt,bin[N],inv[N]; double b[N];
struct node{ int x,y; }a[N];
int main(){
	scanf("%d",&n);
	int i,j,k;
	for (i=bin[0]=1; i<=n; i++) bin[i]=(bin[i-1]<<1)%mod;
	inv[0]=inv[1]=1;
	for (i=2; i<=n; i++) inv[i]=mod-(ll)inv[mod%i]*(mod/i)%mod;
	for (i=1; i<=n; i++) scanf("%d%d",&a[i].x,&a[i].y);
	int ans=bin[n]-1;
	for (i=1; i<=n; i++){
		for (j=1,cnt=0; j<=n; j++)
			if (i!=j) b[++cnt]=min(atan2(a[j].y-a[i].y,a[j].x-a[i].x),atan2(a[i].y-a[j].y,a[i].x-a[j].x));
		sort(b+1,b+cnt+1);
		for (j=k=1; j<=cnt; j=k){
			for (; k<=cnt && abs(b[k]-b[j])<eps; k++);
			ans=(ans-(ll)(bin[k-j+1]-k+j-2)*inv[k-j+1]%mod+mod)%mod;
		}
	}
	printf("%d\n",(ans-n+mod)%mod);
	return 0;
}

### Prompt

In Cpp, your task is to solve 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>
#define ll long long
#define mod 998244353
#define eps 1e-10
#define N 209
using namespace std;

int n,cnt,bin[N],inv[N]; double b[N];
struct node{ int x,y; }a[N];
int main(){
	scanf("%d",&n);
	int i,j,k;
	for (i=bin[0]=1; i<=n; i++) bin[i]=(bin[i-1]<<1)%mod;
	inv[0]=inv[1]=1;
	for (i=2; i<=n; i++) inv[i]=mod-(ll)inv[mod%i]*(mod/i)%mod;
	for (i=1; i<=n; i++) scanf("%d%d",&a[i].x,&a[i].y);
	int ans=bin[n]-1;
	for (i=1; i<=n; i++){
		for (j=1,cnt=0; j<=n; j++)
			if (i!=j) b[++cnt]=min(atan2(a[j].y-a[i].y,a[j].x-a[i].x),atan2(a[i].y-a[j].y,a[i].x-a[j].x));
		sort(b+1,b+cnt+1);
		for (j=k=1; j<=cnt; j=k){
			for (; k<=cnt && abs(b[k]-b[j])<eps; k++);
			ans=(ans-(ll)(bin[k-j+1]-k+j-2)*inv[k-j+1]%mod+mod)%mod;
		}
	}
	printf("%d\n",(ans-n+mod)%mod);
	return 0;
}

```