#include<iostream>
#include<cstdio>
using namespace std;

int N;
int x[200], y[200];
long long mod = 998244353;
long long ans = 0;



int main(){
    cin >> N;
    for(int i = 0; i < N; i++){
        cin >> x[i] >> y[i];
    }
    ans = 1;
    for(int i = 0; i < N; i++){
        ans *= 2;
        ans %= mod;
    }

    ans += mod - 1;
    ans %= mod;
    ans += mod - N;
    ans %= mod;
    for(int i = 0; i < N; i++){
        for(int j = i + 1; j < N; j++){
            int cnt = 0;
            for(int k = j + 1; k < N; k++){
                int dx1 = x[k] - x[i];
                int dx2 = x[k] - x[j];
                int dy1 = y[k] - y[i];
                int dy2 = y[k] - y[j];
                if(dx1*dy2 == dx2*dy1){
                    cnt++;
                }
            }
            int minus = 1;
            for(int k = 0; k < cnt; k++){
                minus *= 2;
                minus %= mod;
            }
            ans += mod - minus;
            ans %= mod;
        }
    }
    cout << ans << endl;
}
### 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<iostream>
#include<cstdio>
using namespace std;

int N;
int x[200], y[200];
long long mod = 998244353;
long long ans = 0;



int main(){
    cin >> N;
    for(int i = 0; i < N; i++){
        cin >> x[i] >> y[i];
    }
    ans = 1;
    for(int i = 0; i < N; i++){
        ans *= 2;
        ans %= mod;
    }

    ans += mod - 1;
    ans %= mod;
    ans += mod - N;
    ans %= mod;
    for(int i = 0; i < N; i++){
        for(int j = i + 1; j < N; j++){
            int cnt = 0;
            for(int k = j + 1; k < N; k++){
                int dx1 = x[k] - x[i];
                int dx2 = x[k] - x[j];
                int dy1 = y[k] - y[i];
                int dy2 = y[k] - y[j];
                if(dx1*dy2 == dx2*dy1){
                    cnt++;
                }
            }
            int minus = 1;
            for(int k = 0; k < cnt; k++){
                minus *= 2;
                minus %= mod;
            }
            ans += mod - minus;
            ans %= mod;
        }
    }
    cout << ans << endl;
}
```