#include <cstdio>
#include <algorithm>

#define x first
#define y second

using namespace std;

const int p = 998244353;

typedef pair<int, int> pii;

pii a[202];

int ccw(pii u, pii v, pii w) {
	return (u.x - v.x) * (u.y - w.y) - (u.y - v.y) * (u.x - w.x);
}

int main() {
	int i, j, k, n, t, r = 0;
	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		scanf("%d%d", &a[i].x, &a[i].y);
	}
	r = n + 1;
	for (i = 0; i < n; i++) for (j = 0; j < i; j++) {
		t = 1;
		for (k = 0; k < j; k++) if (ccw(a[i], a[j], a[k]) == 0) {
			t = (t << 1) % p;
		}
		r = (r + t) % p;
	}
	t = 1;
	for (i = 0; i < n; i++) t = (t << 1) % p;
	printf("%d\n", (t - r + p) % p);
}

### Prompt

Create a solution in cpp for 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>

#define x first
#define y second

using namespace std;

const int p = 998244353;

typedef pair<int, int> pii;

pii a[202];

int ccw(pii u, pii v, pii w) {
	return (u.x - v.x) * (u.y - w.y) - (u.y - v.y) * (u.x - w.x);
}

int main() {
	int i, j, k, n, t, r = 0;
	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		scanf("%d%d", &a[i].x, &a[i].y);
	}
	r = n + 1;
	for (i = 0; i < n; i++) for (j = 0; j < i; j++) {
		t = 1;
		for (k = 0; k < j; k++) if (ccw(a[i], a[j], a[k]) == 0) {
			t = (t << 1) % p;
		}
		r = (r + t) % p;
	}
	t = 1;
	for (i = 0; i < n; i++) t = (t << 1) % p;
	printf("%d\n", (t - r + p) % p);
}

```