#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cmath>

#define For(i, j, k) for(int i = j; i <= k; i++)
#define Forr(i, j, k) for(int i = j; i >= k; i--)

using namespace std;

const int Mod = 998244353;

const int N = 310;

struct Point{
	int x, y;
}P[N];

int n, Pow[N];
double s[N];

int main(){
	scanf("%d", &n);
	Pow[0] = 1;
	For(i, 1, n) scanf("%d%d", &P[i].x, &P[i].y), Pow[i] = Pow[i - 1] * 2 % Mod;
	int ans = Pow[n] - n;
	For(i, 1, n){
		int c = 0;
		For(j, i + 1, n) s[++c] = P[i].x == P[j].x ? 1e10 : double(P[j].y - P[i].y) / double(P[j].x - P[i].x);
		sort(s + 1, s + c + 1);
		For(j, 1, c){
			int r = j;
			while(r < c && fabs(s[r + 1] - s[j]) < 1e-10) ++r;
			ans = (Mod + ans - Pow[r - j + 1] + 1) % Mod;
			j = r;
		}
	}
	printf("%d\n", (ans + Mod - 1) % Mod);
	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 <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cmath>

#define For(i, j, k) for(int i = j; i <= k; i++)
#define Forr(i, j, k) for(int i = j; i >= k; i--)

using namespace std;

const int Mod = 998244353;

const int N = 310;

struct Point{
	int x, y;
}P[N];

int n, Pow[N];
double s[N];

int main(){
	scanf("%d", &n);
	Pow[0] = 1;
	For(i, 1, n) scanf("%d%d", &P[i].x, &P[i].y), Pow[i] = Pow[i - 1] * 2 % Mod;
	int ans = Pow[n] - n;
	For(i, 1, n){
		int c = 0;
		For(j, i + 1, n) s[++c] = P[i].x == P[j].x ? 1e10 : double(P[j].y - P[i].y) / double(P[j].x - P[i].x);
		sort(s + 1, s + c + 1);
		For(j, 1, c){
			int r = j;
			while(r < c && fabs(s[r + 1] - s[j]) < 1e-10) ++r;
			ans = (Mod + ans - Pow[r - j + 1] + 1) % Mod;
			j = r;
		}
	}
	printf("%d\n", (ans + Mod - 1) % Mod);
	return 0;
}
```