#include <bits/stdc++.h>
#define rep(a, b, c) for(int a = (b); a <= (c); ++ a)
#define per(a, b, c) for(int a = (b); a >= (c); -- a)
using namespace std;
template <class T> void rd(T &x){
  x = 0; int f = 1; char ch = getchar();
  while(ch < '0' || ch > '9'){ if(ch == '-') f = -1; ch = getchar(); }
  while(ch >= '0' && ch <= '9') x = (x << 3) + (x << 1) + ch - '0', ch = getchar();
  x *= f;
}

const int mod = 998244353;
const int maxn = 205;
int n;
int x[maxn], y[maxn], pw[maxn];
int ans;

int main(){
  rd(n);
  pw[0] = 1;
  rep(i, 1, n) rd(x[i]), rd(y[i]), pw[i] = pw[i - 1] * 2 % mod;
  int ans = pw[n] - n - 1;
  rep(i, 1, n){
	rep(j, i + 1, n){
	  int cnt = 0;
	  rep(k, j + 1, n){
		if((y[i] - y[k]) * (x[j] - x[k]) == (y[j] - y[k]) * (x[i] - x[k]))
		  cnt ++;
	  }
	  ans = (ans + mod - pw[cnt]) % mod;
	}
  }
  printf("%d\n", ans);
  return 0;
}

### Prompt

Your challenge is to write 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>
#define rep(a, b, c) for(int a = (b); a <= (c); ++ a)
#define per(a, b, c) for(int a = (b); a >= (c); -- a)
using namespace std;
template <class T> void rd(T &x){
  x = 0; int f = 1; char ch = getchar();
  while(ch < '0' || ch > '9'){ if(ch == '-') f = -1; ch = getchar(); }
  while(ch >= '0' && ch <= '9') x = (x << 3) + (x << 1) + ch - '0', ch = getchar();
  x *= f;
}

const int mod = 998244353;
const int maxn = 205;
int n;
int x[maxn], y[maxn], pw[maxn];
int ans;

int main(){
  rd(n);
  pw[0] = 1;
  rep(i, 1, n) rd(x[i]), rd(y[i]), pw[i] = pw[i - 1] * 2 % mod;
  int ans = pw[n] - n - 1;
  rep(i, 1, n){
	rep(j, i + 1, n){
	  int cnt = 0;
	  rep(k, j + 1, n){
		if((y[i] - y[k]) * (x[j] - x[k]) == (y[j] - y[k]) * (x[i] - x[k]))
		  cnt ++;
	  }
	  ans = (ans + mod - pw[cnt]) % mod;
	}
  }
  printf("%d\n", ans);
  return 0;
}

```