#include <bits/stdc++.h>

typedef long long ll;
typedef long long llong;
typedef long double ld;
typedef unsigned long long ull;

using namespace std;

const ll MOD = 998244353;
ll pw(ll a, ll b) {
	ll ans = 1; while (b) {
		while (!(b & 1)) b >>= 1, a = (a * a) % MOD;
		ans = (ans * a) % MOD, --b;
	} return ans;
}

struct point {
	ll x, y;
	point operator-(point a) {
		return {x - a.x, y - a.y};
	}
	ll operator*(point a) {
		return x * a.y - y * a.x;
	}
	bool operator<(point a) {
		return make_pair(x, y) < make_pair(a.x, a.y);
	}
};

int n;
point a[300];


int main() {
	cin >> n;
	for (int i = 0; i < n; ++i)
		cin >> a[i].x >> a[i].y;
	ll ans = 1;
	for (int i = 0; i < n; ++i)
		ans = ans * 2 % MOD;
	ans = (ans - 1 + MOD) % MOD;
	ans = (ans - n + MOD) % MOD;
	for (int i = 0; i < n; ++i)
		for (int j = 0; j < n; ++j) {
			if (!(a[i] < a[j]))
				continue;
			int cc = 0;
			for (int k = 0; k < n; ++k)
				if (a[i] < a[k] && a[k] < a[j] && (a[k] - a[i]) * (a[j] - a[i]) == 0)
					++cc;
			ll mn = pw(2, cc);
			ans = (ans - mn + MOD) % MOD;
		}
	cout << ans << "\n";
	return 0;
}



### Prompt

Your task is to create 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
#include <bits/stdc++.h>

typedef long long ll;
typedef long long llong;
typedef long double ld;
typedef unsigned long long ull;

using namespace std;

const ll MOD = 998244353;
ll pw(ll a, ll b) {
	ll ans = 1; while (b) {
		while (!(b & 1)) b >>= 1, a = (a * a) % MOD;
		ans = (ans * a) % MOD, --b;
	} return ans;
}

struct point {
	ll x, y;
	point operator-(point a) {
		return {x - a.x, y - a.y};
	}
	ll operator*(point a) {
		return x * a.y - y * a.x;
	}
	bool operator<(point a) {
		return make_pair(x, y) < make_pair(a.x, a.y);
	}
};

int n;
point a[300];


int main() {
	cin >> n;
	for (int i = 0; i < n; ++i)
		cin >> a[i].x >> a[i].y;
	ll ans = 1;
	for (int i = 0; i < n; ++i)
		ans = ans * 2 % MOD;
	ans = (ans - 1 + MOD) % MOD;
	ans = (ans - n + MOD) % MOD;
	for (int i = 0; i < n; ++i)
		for (int j = 0; j < n; ++j) {
			if (!(a[i] < a[j]))
				continue;
			int cc = 0;
			for (int k = 0; k < n; ++k)
				if (a[i] < a[k] && a[k] < a[j] && (a[k] - a[i]) * (a[j] - a[i]) == 0)
					++cc;
			ll mn = pw(2, cc);
			ans = (ans - mn + MOD) % MOD;
		}
	cout << ans << "\n";
	return 0;
}



```