#include<iostream>
#include<string.h>
#include<stdio.h>
#include<algorithm>
#define mod 998244353 
#define maxn 505
using namespace std;
int n, ans, x[maxn], y[maxn], pw[maxn];

int main(){
    scanf( "%d", &n );
    pw[0] = 1;
    for( int i = 1; i <= n; i ++ ) pw[i] = ( long long ) pw[i - 1] * 2 % mod;
    for( int i = 1; i <= n; i ++ ) scanf( "%d%d", &x[i], &y[i] );
    ans = ( pw[n] - n - 1 - n * ( n - 1 ) / 2 + mod ) % mod;
    for( int i = 1; i <= n; i ++ ) {
        for( int j = i + 1; j <= n; j ++ ) {
            int tmp = 0;
            for( int k = j + 1; k <= n; k ++ ) {
                if( ( y[j] - y[i] ) * ( x[k] - x[j] ) == ( y[k] - y[j] ) * ( x[j] - x[i] ) ) tmp ++;
            }
            ans = ( ans + mod + 1 - pw[tmp] ) % mod;
        }
    }
    printf( "%d", ans );
}
### Prompt

In CPP, your task is to solve 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<string.h>
#include<stdio.h>
#include<algorithm>
#define mod 998244353 
#define maxn 505
using namespace std;
int n, ans, x[maxn], y[maxn], pw[maxn];

int main(){
    scanf( "%d", &n );
    pw[0] = 1;
    for( int i = 1; i <= n; i ++ ) pw[i] = ( long long ) pw[i - 1] * 2 % mod;
    for( int i = 1; i <= n; i ++ ) scanf( "%d%d", &x[i], &y[i] );
    ans = ( pw[n] - n - 1 - n * ( n - 1 ) / 2 + mod ) % mod;
    for( int i = 1; i <= n; i ++ ) {
        for( int j = i + 1; j <= n; j ++ ) {
            int tmp = 0;
            for( int k = j + 1; k <= n; k ++ ) {
                if( ( y[j] - y[i] ) * ( x[k] - x[j] ) == ( y[k] - y[j] ) * ( x[j] - x[i] ) ) tmp ++;
            }
            ans = ( ans + mod + 1 - pw[tmp] ) % mod;
        }
    }
    printf( "%d", ans );
}
```