#include <iostream>
#include <complex>

using namespace std;

const int MAXN = 310;
const int MOD = 998244353;

typedef complex<int> Point;

long long cross(Point a, Point b)
{
	return a.real() * b.imag() - a.imag() * b.real();
}

int add(long long a, long long b)
{
	return (a + b + MOD) % MOD;
}

int mul(long long a, long long b)
{
	return (a * b) % MOD;
}

Point a[MAXN];
int pw[MAXN];

int main()
{
	int n;
	cin >> n;
	for (int i = 0; i < n; i++)
	{
		int x, y;
		cin >> x >> y;
		a[i] = Point(x, y);
	}
	pw[0] = 1;
	for (int i = 0; i < n; i++)
		pw[i + 1] = mul(pw[i], 2);
	int res = 0;
	for (int i = 0; i < n; i++)
		for (int j = i + 1; j < n; j++)
		{
			int cnt = 0;
			for (int k = j + 1; k < n; k++)
				if (cross(a[k] - a[i], a[j] - a[i]) != 0)
				{
					cnt++;
					res = add(res, pw[n - j - 1 - cnt]);
				}
		}
	cout << res << endl;
}
### 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 <iostream>
#include <complex>

using namespace std;

const int MAXN = 310;
const int MOD = 998244353;

typedef complex<int> Point;

long long cross(Point a, Point b)
{
	return a.real() * b.imag() - a.imag() * b.real();
}

int add(long long a, long long b)
{
	return (a + b + MOD) % MOD;
}

int mul(long long a, long long b)
{
	return (a * b) % MOD;
}

Point a[MAXN];
int pw[MAXN];

int main()
{
	int n;
	cin >> n;
	for (int i = 0; i < n; i++)
	{
		int x, y;
		cin >> x >> y;
		a[i] = Point(x, y);
	}
	pw[0] = 1;
	for (int i = 0; i < n; i++)
		pw[i + 1] = mul(pw[i], 2);
	int res = 0;
	for (int i = 0; i < n; i++)
		for (int j = i + 1; j < n; j++)
		{
			int cnt = 0;
			for (int k = j + 1; k < n; k++)
				if (cross(a[k] - a[i], a[j] - a[i]) != 0)
				{
					cnt++;
					res = add(res, pw[n - j - 1 - cnt]);
				}
		}
	cout << res << endl;
}
```