#include<iostream>
using namespace std;

#define LL long long
const int N = 211;
const int mod = 998244353;
int n;
LL base[N];

struct ddd {
	int x, y;
}nd[N];

LL sq(LL x) { return x * x; }

bool check(LL x1, LL y1, LL x2, LL y2) {
	LL a = x1 * x2 + y1 * y2;
	LL b = (sq(x1) + sq(y1)) * (sq(x2) + sq(y2));
	return a > 0 && b == sq(a);
}
int main() {
	cin >> n;
	for (int i = 1; i <= n; i++) {
		scanf("%d%d", &nd[i].x, &nd[i].y);
	}
	base[0] = 1;
	for (int i = 1; i <= 200; i++)base[i] = base[i - 1] * 2 % mod;
	LL ans = (base[n] - 1 - n + mod) % mod;
	for (int i = 2; i <= n; i++) {
		for (int j = 1; j < i; j++) {
			int tot = 0;
			for (int k = 1; k <= n; k++) {
				if (i == k || j == k)continue;
				if (check(nd[i].x - nd[k].x, nd[i].y - nd[k].y, nd[k].x - nd[j].x, nd[k].y - nd[j].y))tot++;
			}
			ans = (ans + mod - base[tot]) % mod;
		}
	}
	cout << ans << endl;
	return 0;
}

### 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<iostream>
using namespace std;

#define LL long long
const int N = 211;
const int mod = 998244353;
int n;
LL base[N];

struct ddd {
	int x, y;
}nd[N];

LL sq(LL x) { return x * x; }

bool check(LL x1, LL y1, LL x2, LL y2) {
	LL a = x1 * x2 + y1 * y2;
	LL b = (sq(x1) + sq(y1)) * (sq(x2) + sq(y2));
	return a > 0 && b == sq(a);
}
int main() {
	cin >> n;
	for (int i = 1; i <= n; i++) {
		scanf("%d%d", &nd[i].x, &nd[i].y);
	}
	base[0] = 1;
	for (int i = 1; i <= 200; i++)base[i] = base[i - 1] * 2 % mod;
	LL ans = (base[n] - 1 - n + mod) % mod;
	for (int i = 2; i <= n; i++) {
		for (int j = 1; j < i; j++) {
			int tot = 0;
			for (int k = 1; k <= n; k++) {
				if (i == k || j == k)continue;
				if (check(nd[i].x - nd[k].x, nd[i].y - nd[k].y, nd[k].x - nd[j].x, nd[k].y - nd[j].y))tot++;
			}
			ans = (ans + mod - base[tot]) % mod;
		}
	}
	cout << ans << endl;
	return 0;
}

```