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| #include <bits/stdc++.h>
#define int long long
#define repi(i,a,b) for(int i = (a); i < (b); i++)
#define rep(i,a) repi(i,0,a)
#define all(u) (u).begin(),(u).end()
#define pb push_back
#define mp make_pair
#define EPS 1e-10
#define PI acos(-1.0)
using namespace std;
typedef complex<double> P;
typedef vector<P> G;
double dot(const P& a, const P& b) { return real(conj(a)*b); }
struct L {
P a, b;
L(const P &a, const P &b) : a(a), b(b){ }
};
P projection(const L &l, const P &p) {
double t = dot(p-l.a, l.a-l.b) / norm(l.a-l.b);
return l.a + t*(l.a-l.b);
}
P reflection(const L &l, const P &p) { return p + 2.0 * (projection(l, p) - p);}
int N, ans;
P s;
G g;
bool used[10];
vector<L> mirrs;
bool input(){
cin >> N;
if(!N) return 0;
ans = 0;
g.clear();
memset(used,0,sizeof(used));
double a, b;
cin >> a >> b;
s = P(a,b);
rep(i,N){
cin >> a >> b;
g.pb(P(a,b));
}
return 1;
}
void ref_points(int cur){
L mirror = L(g[cur], g[(cur+1)%N]);
rep(j,N) if(j != cur && j != (cur + 1) % N) g[j] = reflection(mirror, g[j]);
}
void swap(P &p){
double s = p.real();
double t = p.imag();
p = P(t, s);
}
void realmax(P &p, P q){
double s = p.real();
double t = q.real();
p = P(max(s, t), p.imag());
}
void imagmin(P &p, P q){
double s = p.imag();
double t = q.imag();
p = P(p.real(), min(s, t));
}
bool ok(){
vector<P> res(2);
res[0] = P(-PI,0);
res[1] = P(0, PI);
int T = mirrs.size();
rep(i,T){
P args = P(arg(mirrs[i].a - s), arg(mirrs[i].b - s));
if(args.real() > args.imag()) swap(args);
P sect[2];
if(args.imag() - args.real() > PI + EPS) {
sect[0] = P(-PI, args.real());
sect[1] = P(args.imag(), PI);
}
else if(args.real() < 0 && args.imag() < 0){
sect[0] = P(args.real(), args.imag());
sect[1] = P(0, 0);
}
else if(args.real() < 0 && args.imag() >= 0){
sect[0] = P(args.real(), 0);
sect[1] = P(0, args.imag());
}
else {
sect[0] = P(0, 0);
sect[1] = P(args.real(), args.imag());
}
rep(i,res.size()){
realmax(res[i], sect[i]);
imagmin(res[i], sect[i]);
}
}
rep(i,res.size()) if(res[i].imag() - res[i].real() < EPS) {
res.erase(res.begin() + i, res.begin() + i + 1);
i--;
}
return res.size();
}
void dfs(){
if(mirrs.size() == N){
if(ok()) ans++;
return;
}
rep(i,N) if(!used[i]) {
used[i] = 1;
mirrs.pb(L(g[i],g[(i+1)%N]));
ref_points(i);
dfs();
ref_points(i);
mirrs.pop_back();
used[i] = 0;
}
}
int solve(){
dfs();
return ans;
}
signed main(){
while(input()){ cout << solve() << endl;}
return 0;
}
|
