#include<bits/stdc++.h>
using namespace std;

const int N = 205, P = 998244353;

int n, h[N], t;
bool v[N][N];

int qp (int a, int b) { int c = 1; for (; b; b >>= 1, a = 1ll * a * a % P) if (b & 1) c = 1ll * c * a % P; return c; }

struct Vector {
	int x, y;
}p[N];

Vector operator - (const Vector &A, const Vector &B) { return Vector{A.x - B.x, A.y - B.y}; }
int operator * (const Vector &A, const Vector &B) { return A.x * B.y - A.y * B.x; }

int main () {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) scanf("%d%d", &p[i].x, &p[i].y);
	int ans = qp(2, n) - 1 - n;
	for (int i = 1; i <= n; ++i) {
		h[1] = i;
		for (int j = i + 1; j <= n; ++j) if (!v[i][j]) {
			h[t = 2] = j;
			for (int k = j + 1; k <= n; ++k) if ((p[k] - p[i]) * (p[j] - p[i]) == 0) h[++t] = k;
			ans = (ans - qp(2, t) + 1 + t) % P;
			for (int a = 1; a <= t; ++a) for (int b = 1; b <= t; ++b) v[h[a]][h[b]] = 1;
		}
	}
	printf("%d\n", (ans + P) % P);
	return 0;
}
### Prompt

In Cpp, your task is to solve 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>
using namespace std;

const int N = 205, P = 998244353;

int n, h[N], t;
bool v[N][N];

int qp (int a, int b) { int c = 1; for (; b; b >>= 1, a = 1ll * a * a % P) if (b & 1) c = 1ll * c * a % P; return c; }

struct Vector {
	int x, y;
}p[N];

Vector operator - (const Vector &A, const Vector &B) { return Vector{A.x - B.x, A.y - B.y}; }
int operator * (const Vector &A, const Vector &B) { return A.x * B.y - A.y * B.x; }

int main () {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) scanf("%d%d", &p[i].x, &p[i].y);
	int ans = qp(2, n) - 1 - n;
	for (int i = 1; i <= n; ++i) {
		h[1] = i;
		for (int j = i + 1; j <= n; ++j) if (!v[i][j]) {
			h[t = 2] = j;
			for (int k = j + 1; k <= n; ++k) if ((p[k] - p[i]) * (p[j] - p[i]) == 0) h[++t] = k;
			ans = (ans - qp(2, t) + 1 + t) % P;
			for (int a = 1; a <= t; ++a) for (int b = 1; b <= t; ++b) v[h[a]][h[b]] = 1;
		}
	}
	printf("%d\n", (ans + P) % P);
	return 0;
}
```