#include <bits/stdc++.h>
#define MOD 998244353
using namespace std;
typedef long long ll;
int n, cnt, X[210], Y[210], P[210] = { 1 };
bool done[210][210];
int norm(int x) {
	return (x + MOD) % MOD;
}
bool linear(int a, int b, int c) {
	return (X[a] - X[c])*(Y[b] - Y[c]) - (Y[a] - Y[c])*(X[b] - X[c]) == 0;
}
int subset(int x) {
	return norm(P[x] - x - 1);
}
void count(int v, int u) {
	if (done[v][u]) return;
	vector<int> V;
	for (int i = 1; i <= n; i++)
		if (linear(u, v, i))
			V.push_back(i);
	int m = V.size();
	for (int i = 0; i<m; i++)
		for (int j = 0; j<m; j++)
			done[V[i]][V[j]] = true;
	cnt = (cnt + subset(m)) % MOD;
}
int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
		P[i] = (P[i - 1] * 2) % MOD;
	for (int i = 1; i <= n; i++)
		scanf("%d%d", X + i, Y + i);
	for (int i = 1; i <= n; i++)
		for (int j = i + 1; j <= n; j++)
			count(i, j);
	int ans = subset(n);
	printf("%d", norm(ans - cnt));
	return 0;
}
### Prompt

Please formulate 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>
#define MOD 998244353
using namespace std;
typedef long long ll;
int n, cnt, X[210], Y[210], P[210] = { 1 };
bool done[210][210];
int norm(int x) {
	return (x + MOD) % MOD;
}
bool linear(int a, int b, int c) {
	return (X[a] - X[c])*(Y[b] - Y[c]) - (Y[a] - Y[c])*(X[b] - X[c]) == 0;
}
int subset(int x) {
	return norm(P[x] - x - 1);
}
void count(int v, int u) {
	if (done[v][u]) return;
	vector<int> V;
	for (int i = 1; i <= n; i++)
		if (linear(u, v, i))
			V.push_back(i);
	int m = V.size();
	for (int i = 0; i<m; i++)
		for (int j = 0; j<m; j++)
			done[V[i]][V[j]] = true;
	cnt = (cnt + subset(m)) % MOD;
}
int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
		P[i] = (P[i - 1] * 2) % MOD;
	for (int i = 1; i <= n; i++)
		scanf("%d%d", X + i, Y + i);
	for (int i = 1; i <= n; i++)
		for (int j = i + 1; j <= n; j++)
			count(i, j);
	int ans = subset(n);
	printf("%d", norm(ans - cnt));
	return 0;
}
```