#include <stdio.h>#include <cstring>#include <string>#include <vector>#include <cmath>#include <queue>using namespace std;#define REP(i, x) for (int i = 0;i < x;i++)#define MP(x, y) make_pair(x, y)const double eps = 1e-10;struct pt{ double x, y; pt (double _x = 0,double _y = 0): x(_x), y(_y) {} pt operator + (const pt a) { return pt(x + a.x, y + a.y); } pt operator - (const pt a) { return pt(x - a.x, y - a.y); } pt operator * (const double a) { return pt(x*a, y*a); } double len() { return sqrt(x*x+y*y); } void rd() { scanf("%lf%lf",&x,&y); } void write() { printf("(%.2f,%.2f)",x,y); }};double det(pt a,pt b) { return a.x*b.y - a.y*b.x; }double dot(pt a,pt b) { return a.x*b.x + a.y*b.y; }double dis(pt a,pt b) { return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y)); }double sgn(double x) { return x > eps? 1 : x < -eps? -1 : 0; }double point_line_dis(pt x,pt a, pt b){ return fabs(det(a-x,b-x) / dis(a,b));}double point_seg_dis(pt x,pt a,pt b){ if (sgn(dot(b-a,x-a)) * sgn(dot(b-a,x-b)) < 0)return point_line_dis(x, a, b);return min(dis(a,x),dis(b,x));}const int V = 3300;const double INFI = 1e10;pair<pt, pt> line[V];pt o;int n;vector< pair<int, double> > adj[V];struct node{double dis; int v;node(double _dis = 0,int _v = 0) : dis(_dis), v(_v){}bool operator <(const node &a)const{return dis > a.dis + eps;}};priority_queue<node> Q;bool use[V];double dist[V];void build(pt o, int id){ pt l = o + pt(-1, 0); pt r = o + pt(1, 0); adj[id].clear(); bool first = true; for (int i=0;i<n;i++) if (line[i].second.y < o.y - eps) { pt a = line[i].first; pt b = line[i].second; double deltay = line[i].second.y - o.y; if (first) {l = a; r = b; first = false;}l = o + (l-o) * (deltay / (l-o).y);r = o + (r-o) * (deltay / (r-o).y);if (det(l-o, a-o) > eps) l = a; if (det(r-o, b-o) < -eps) r = b; if (det(l-o, r-o) < -eps) return; if (sgn(det(l-o, a-o)) == 0) adj[id].push_back( MP(i, dis(o, a)) ); if (sgn(det(r-o, b-o)) == 0) adj[id].push_back( MP(i+n, dis(o, b)) ); } double left = point_seg_dis(o, l ,r); adj[id].push_back( MP(2*n+1, left) );}double djstra(int s){ while (!Q.empty()) Q.pop(); Q.push(node(0, s)); for (int i=0;i<V;i++) dist[i] = INFI, use[i] = false;dist[s] = 0;while (!Q.empty()) { int v = Q.top().v; Q.pop();if (v == 2*n+1) return dist[v]; if (use[v]) continue; use[v] = true; for (int i=0;i<adj[v].size();i++) if (dist[v] + adj[v][i].second < dist[ adj[v][i].first ] - eps) { int u = adj[v][i].first; dist[u] = dist[v] + adj[v][i].second; Q.push(node(dist[u], u)); } } return -1;}double solve(){ build(o, 2*n); for (int i=0;i<n;i++) { build(line[i].first, i); build(line[i].second, i+n); }return djstra(2*n);}int cas = 0;int main(){int test = 0;double x1, x2, y; while (1) {scanf("%d",&n); if (n == 0) break;o.rd(); REP(i, n){ scanf("%lf%lf%lf",&y,&x1,&x2); line[i].first = pt(x1, y); line[i].second = pt(x2, y); } test += n; if (test > 10000) test /= 0; printf("%.10fn",solve()); }}
