#include <cstring>
#include <algorithm>
#include <cstdio>

using namespace std;
const int MAXN = 210;
const int MOD = 998244353;
int nowarn;

int n, x[MAXN], y[MAXN];
int ans, pw[MAXN];

bool OnLine( int i, int j, int k ) {
	if( y[i] > y[j] ) swap(i, j);
	if( y[k] < y[i] || y[k] > y[j] ) return false;
	if( x[i] > x[j] ) swap(i, j);
	if( x[k] < x[i] || x[k] > x[j] ) return false;
	int vx = x[k] - x[i], vy = y[k] - y[i];
	int wx = x[k] - x[j], wy = y[k] - y[j];
	return vx*wy - vy*wx == 0;
}

int main() {
	nowarn = scanf( "%d", &n );
	for( int i = 0; i < n; ++i )
		nowarn = scanf( "%d%d", x+i, y+i );
	pw[0] = 1;
	for( int i = 1; i <= n; ++i )
		pw[i] = pw[i-1] * 2 % MOD;
	ans = (pw[n] - n + MOD) % MOD;
	for( int i = 0; i < n; ++i )
		for( int j = i+1; j < n; ++j ) {
			int cnt = 0;
			for( int k = 0; k < n; ++k )
				if( k != i && k != j && OnLine(i, j, k) )
					++cnt;
			ans = (ans - pw[cnt] + MOD) % MOD;
		}
	printf( "%d\n", (ans - 1 + MOD) % MOD );
	return 0;
}

### Prompt

Generate 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 <cstring>
#include <algorithm>
#include <cstdio>

using namespace std;
const int MAXN = 210;
const int MOD = 998244353;
int nowarn;

int n, x[MAXN], y[MAXN];
int ans, pw[MAXN];

bool OnLine( int i, int j, int k ) {
	if( y[i] > y[j] ) swap(i, j);
	if( y[k] < y[i] || y[k] > y[j] ) return false;
	if( x[i] > x[j] ) swap(i, j);
	if( x[k] < x[i] || x[k] > x[j] ) return false;
	int vx = x[k] - x[i], vy = y[k] - y[i];
	int wx = x[k] - x[j], wy = y[k] - y[j];
	return vx*wy - vy*wx == 0;
}

int main() {
	nowarn = scanf( "%d", &n );
	for( int i = 0; i < n; ++i )
		nowarn = scanf( "%d%d", x+i, y+i );
	pw[0] = 1;
	for( int i = 1; i <= n; ++i )
		pw[i] = pw[i-1] * 2 % MOD;
	ans = (pw[n] - n + MOD) % MOD;
	for( int i = 0; i < n; ++i )
		for( int j = i+1; j < n; ++j ) {
			int cnt = 0;
			for( int k = 0; k < n; ++k )
				if( k != i && k != j && OnLine(i, j, k) )
					++cnt;
			ans = (ans - pw[cnt] + MOD) % MOD;
		}
	printf( "%d\n", (ans - 1 + MOD) % MOD );
	return 0;
}

```