#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 210, mod = 998244353;
int n;
int x[N], y[N];
ll ans;
ll p[N];
int main()
{
	scanf("%d", &n);
	for(int i = 1; i <= n; ++i) scanf("%d%d", &x[i], &y[i]);
	p[0] = 1;
	for(int i = 1; i <= n; ++i) p[i] = (p[i - 1] << 1) % mod;
	ans = p[n] - n * (n - 1) / 2 - n - 1;
	for(int i = 1; i <= n; ++i)  
		for(int j = i + 1; j <= n; ++j)
		{
			int cnt = 0;   
			for(int k = j + 1; k <= n; ++k) if((y[k] - y[i]) * (x[k] - x[j]) == (y[k] - y[j]) * (x[k] - x[i])) ++cnt;
			ans = ((ans - p[cnt] + 1) % mod + mod) % mod;
		}
	cout << ans;
	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>
using namespace std;
typedef long long ll;
const int N = 210, mod = 998244353;
int n;
int x[N], y[N];
ll ans;
ll p[N];
int main()
{
	scanf("%d", &n);
	for(int i = 1; i <= n; ++i) scanf("%d%d", &x[i], &y[i]);
	p[0] = 1;
	for(int i = 1; i <= n; ++i) p[i] = (p[i - 1] << 1) % mod;
	ans = p[n] - n * (n - 1) / 2 - n - 1;
	for(int i = 1; i <= n; ++i)  
		for(int j = i + 1; j <= n; ++j)
		{
			int cnt = 0;   
			for(int k = j + 1; k <= n; ++k) if((y[k] - y[i]) * (x[k] - x[j]) == (y[k] - y[j]) * (x[k] - x[i])) ++cnt;
			ans = ((ans - p[cnt] + 1) % mod + mod) % mod;
		}
	cout << ans;
	return 0;
}

```