#include <cstdio>
#include <algorithm>
using namespace std;

const int MAXN = 205;
const int MOD = 998244353;

int N;
int x[MAXN], y[MAXN];
int pot[MAXN];

void load() {
	scanf("%d", &N);
	for (int i = 0; i < N; i++)
		scanf("%d%d", x + i, y + i);
}

inline int add(int x, int y) {
	x += y;
	if (x >= MOD)	
		x -= MOD;
	else if (x < 0)
		x += MOD;
	return x;
}

int ccw(int a, int b, int c) {
	return x[a] * (y[b] - y[c]) + x[b] * (y[c] - y[a]) + x[c] * (y[a] - y[b]);
}

bool in_range(int a, int b, int c) {
	return c >= min(a, b) && c <= max(a, b);
}

int solve() {
	pot[0] = 1;
	for (int i = 1; i <= N; i++)
		pot[i] = add(pot[i - 1], pot[i - 1]);	
	
	int sol = add(pot[N], -N - 1);
	for (int i = 0; i < N; i++)
		for (int j = 0; j < i; j++) {
			int cnt = 0;
			for (int k = 0; k < N; k++)
				cnt += k != i && k != j && !ccw(i, j, k) && in_range(x[i], x[j], x[k]) && in_range(y[i], y[j], y[k]);
			sol = add(sol, -pot[cnt]);
		}
	
	return sol;
}

int main() {
	load();
	printf("%d\n", solve());
	return 0;
}
### 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 <cstdio>
#include <algorithm>
using namespace std;

const int MAXN = 205;
const int MOD = 998244353;

int N;
int x[MAXN], y[MAXN];
int pot[MAXN];

void load() {
	scanf("%d", &N);
	for (int i = 0; i < N; i++)
		scanf("%d%d", x + i, y + i);
}

inline int add(int x, int y) {
	x += y;
	if (x >= MOD)	
		x -= MOD;
	else if (x < 0)
		x += MOD;
	return x;
}

int ccw(int a, int b, int c) {
	return x[a] * (y[b] - y[c]) + x[b] * (y[c] - y[a]) + x[c] * (y[a] - y[b]);
}

bool in_range(int a, int b, int c) {
	return c >= min(a, b) && c <= max(a, b);
}

int solve() {
	pot[0] = 1;
	for (int i = 1; i <= N; i++)
		pot[i] = add(pot[i - 1], pot[i - 1]);	
	
	int sol = add(pot[N], -N - 1);
	for (int i = 0; i < N; i++)
		for (int j = 0; j < i; j++) {
			int cnt = 0;
			for (int k = 0; k < N; k++)
				cnt += k != i && k != j && !ccw(i, j, k) && in_range(x[i], x[j], x[k]) && in_range(y[i], y[j], y[k]);
			sol = add(sol, -pot[cnt]);
		}
	
	return sol;
}

int main() {
	load();
	printf("%d\n", solve());
	return 0;
}
```