#include <iostream>
#include <bits/stdc++.h>
using namespace std;
const int maxn = 255;
const int mod = 998244353;
struct node
{
    int x,y;
};
node a[maxn];
int cf[maxn];
int n;
int ans;
void init()
{
    cf[0]=1;
    for(int i=0;i<n;i++)
    {
        cf[i+1]=(cf[i]*2)%mod;
    }
    ans=cf[n]-(n+1);
}
int main()
{
    cin>>n;
    for(int i=0;i<n;i++)
    {
        cin>>a[i].x>>a[i].y;
    }
    init();
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<i;j++)
        {
            int tot=0;
            for(int k=0;k<j;k++)
            {
                int l1=(a[i].x-a[j].x)*(a[i].y-a[k].y);
                int l2=(a[i].x-a[k].x)*(a[i].y-a[j].y);
                if(l1==l2)
                    tot++;
            }
            ans-=cf[tot];
            ans+=mod;
            ans%=mod;
        }

    }
    cout << ans << endl;
    return 0;
}

### 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 <bits/stdc++.h>
using namespace std;
const int maxn = 255;
const int mod = 998244353;
struct node
{
    int x,y;
};
node a[maxn];
int cf[maxn];
int n;
int ans;
void init()
{
    cf[0]=1;
    for(int i=0;i<n;i++)
    {
        cf[i+1]=(cf[i]*2)%mod;
    }
    ans=cf[n]-(n+1);
}
int main()
{
    cin>>n;
    for(int i=0;i<n;i++)
    {
        cin>>a[i].x>>a[i].y;
    }
    init();
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<i;j++)
        {
            int tot=0;
            for(int k=0;k<j;k++)
            {
                int l1=(a[i].x-a[j].x)*(a[i].y-a[k].y);
                int l2=(a[i].x-a[k].x)*(a[i].y-a[j].y);
                if(l1==l2)
                    tot++;
            }
            ans-=cf[tot];
            ans+=mod;
            ans%=mod;
        }

    }
    cout << ans << endl;
    return 0;
}

```