Problem: Alice and Bob are in love with each other, but they have difficulty going out on a date - Alice is a very busy graduate student at the ACM university.

For this reason, Bob came to the ACM university to meet her on a day. He tried to reach the meeting spot but got lost because the campus of the university was very large. Alice talked with him via mobile phones and identified his current location exactly. So she told him to stay there and decided to go to the place where she would be visible to him without interruption by buildings.

The campus can be considered as a two-dimensional plane and all buildings as rectangles whose edges are parallel to x-axis or y-axis. Alice and Bob can be considered as points. Alice is visible to Bob if the line segment connecting them does not intersect the interior of any building. Note that she is still visible even if the line segment touches the borders of buildings.

Since Alice does not like to walk, she wants to minimize her walking distance. Can you write a program that finds the best route for her?

<image>

Figure 1: Example Situation



Input

The input contains multiple datasets. The end of the input is indicated by a line containing a single zero. Each dataset is formatted as follows.


N
x11 y11 x12 y12
x21 y21 x22 y22
...
xN1 yN1 xN2 yN2
Ax Ay Bx By


N (0 < N ≤ 30) is the number of buildings. The i-th building is given by its bottom left corner (xi1 , yi1) and up right corner (xi2, yi2 ). (Ax, Ay) is the location of Alice and (Bx, By) is that of Bob. All integers xi1, yi1, xi2, yi2, Ax, Ay, Bx and By are between -10000 and 10000, inclusive. You may assume that no building touches or overlaps other buildings.

Output

For each dataset, output a separate line containing the minimum distance Alice has to walk.

The value may contain an error less than or equal to 0.001. You may print any number of digits after the decimal point.

Example

Input

1
3 3 7 7
2 2 8 2
2
2 5 5 9
6 1 9 5
1 5 10 5
2
2 1 3 2
2 3 3 4
1 1 4 4
1
3 3 7 7
1 5 9 5
1
3 3 7 7
1 5 8 5
1
3 3 7 7
1 5 10 5
0


Output

0.000
0.000
0.000
5.657
6.406
4.992

Solution (in CPP):

Solution:
/* 
方針
0. 初期状態で既にAliceが見えているか判定 =(YES)=> 0.000 と出力して終わる
1. Bombと長方形の角を結ぶ線分を列挙
   線分は建物の角とぶつかるor平行であるならそのまま伸ばしていく ( 建物につっこんだら終了 )
2. Aliceから各点 ( 建物の角、線分の端点 ) への最短距離を求める
3. 各点から直接到達可能なBombの線分をみつけ、その点までの距離 + その点からBombの線分までの最短距離を計算し、最も短いものを記録
 */

#include<bits/stdc++.h>

#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define EPS (1e-5)
#define equals(a,b) (fabs((a)-(b))<EPS)

using namespace std;

static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

bool  LT(double a,double b) { return !equals(a,b) && a < b; }
bool LTE(double a,double b) { return  equals(a,b) || a < b; }

class Point{
public:
  double x,y;
  Point(double x = 0,double y = 0): x(x),y(y){}
  Point operator + (const Point &p){return Point(x+p.x,y+p.y);}
  Point operator - (const Point &p){return Point(x-p.x,y-p.y);}
  Point operator * (double a){return Point(a*x,a*y);}
  Point operator / (double a){return Point(x/a,y/a);}
  Point operator * (const Point &a){ return Point(x * a.x - y * a.y, x * a.y + y * a.x); }
  bool operator < (const Point& p) const{ return !equals(x,p.x)?x<p.x:(!equals(y,p.y)&&y<p.y); }
  bool operator == (const Point& p)const{ return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS; }
};

struct Segment{
  Point p1,p2;
  Segment(Point p1 = Point(),Point p2 = Point()):p1(p1),p2(p2){}
  bool operator <  (const Segment& s) const { return ( p1 == s.p1 ) ? p2 < s.p2 : p1 < s.p1; }
  bool operator == (const Segment& p) const { return ( p.p1 == p1 && p.p2 == p2 ) || ( p.p1 == p2 && p.p2 == p1 ); }
};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

double dot(const Point &a,const Point &b){ return a.x*b.x + a.y*b.y; }
double cross(const Point &a,const Point &b){ return a.x*b.y - a.y*b.x; }
double norm(const Point &a){ return a.x*a.x+a.y*a.y; }
double abs(const Point &a){ return sqrt(norm(a)); }

int ccw(Point p0,Point p1,Point p2){
  Point a = p1-p0;
  Point b = p2-p0;
  if(cross(a,b) > EPS)return COUNTER_CLOCKWISE;
  if(cross(a,b) < -EPS)return CLOCKWISE;
  if(dot(a,b) < -EPS)return ONLINE_BACK;
  if(norm(a) < norm(b))return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersectSS(Line s, Line t) {
  return ccw(s.p1,s.p2,t.p1)*ccw(s.p1,s.p2,t.p2) <= 0 &&
         ccw(t.p1,t.p2,s.p1)*ccw(t.p1,t.p2,s.p2) <= 0;
}

bool intersectSP(Line s, Point p) {
  return abs(s.p1-p)+abs(s.p2-p)-abs(s.p2-s.p1) < EPS; // triangle inequality
}

Point projection(Line l,Point p) {
  double t = dot(p-l.p1, l.p1-l.p2) / norm(l.p1-l.p2);
  return l.p1 + (l.p1-l.p2)*t;
}

Point reflection(Line l,Point p) {
  return p + (projection(l, p) - p) * 2;
}

double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

Point nearest_point(Segment seg,Point p){
  Point r = projection(seg,p);
  if( intersectSP(seg,r) ) return r;
  if( LT(abs(seg.p1-p),abs(seg.p2-p)) ) return seg.p1;
  return seg.p2;
}

Point crosspoint(Line l,Line m){
  double A = cross(l.p2-l.p1,m.p2-m.p1);
  double B = cross(l.p2-l.p1,l.p2-m.p1);
  if(abs(A) < EPS && abs(B) < EPS){
    vector<Point> vec;
    vec.push_back(l.p1),vec.push_back(l.p2),vec.push_back(m.p1),vec.push_back(m.p2);
    sort(vec.begin(),vec.end());
    assert(vec[1] == vec[2]); //同じセグメントかもよ
    return vec[1];
  }
  if(abs(A) < EPS)assert(false);
  return m.p1 + (m.p2-m.p1)*(B/A);
}

double cross3p(Point p,Point q,Point r){ return (r.x-q.x) * (p.y -q.y) - (r.y - q.y) * (p.x - q.x); }
  
bool collinear(Point p,Point q,Point r){ return fabs(cross3p(p,q,r)) < EPS; }
  
 
bool onSegment(Point p,Point q,Point r){
  return collinear(p,q,r) && equals(sqrt(pow(p.x-r.x,2)+pow(p.y-r.y,2)) + sqrt(pow(r.x-q.x,2) + pow(r.y-q.y,2) ),sqrt(pow(p.x-q.x,2)+pow(p.y-q.y,2)) ) ;
}

  
//多角形poly内（線分上も含む）に点pが存在するかどうは判定する  
inline bool inPolygon(Polygon poly,Point p,int on) {
  if( LT(poly[0].x,p.x) && LT(p.x,poly[3].x) && LT(poly[0].y,p.y) && LT(p.y,poly[1].y) ) return true;
  return false;
}  

const double DINF = 1e20;
const int MAX_N = 40;
int N;
Point ps[40][2];
Point A,B;

Point vir;
bool comp_dist(const Point &p1,const Point &p2){
  return LT(abs(vir-p1),abs(vir-p2));
}

// target_segがtriesのいづれかと交差しているか? true -> 交差してる false -> してない
bool intersect_checker(const vector<Polygon>& tries,Segment target_seg){
  rep(i,tries.size()){
    vector<Point> vp;
    vp.push_back(target_seg.p1);
    vp.push_back(target_seg.p2);
    rep(j,tries[i].size()){
      Segment seg = Segment(tries[i][j],tries[i][(j+1)%tries[i].size()]);
      if( equals(cross(target_seg.p1-target_seg.p2,seg.p1-seg.p2),0.0) ) {
        if( onSegment(target_seg.p1,target_seg.p2,seg.p1) ) vp.push_back(seg.p1);
        if( onSegment(target_seg.p1,target_seg.p2,seg.p2) ) vp.push_back(seg.p2);
      } else {
        if( intersectSS(target_seg,seg) ) vp.push_back(crosspoint(target_seg,seg));
      }
    }
    sort(vp.begin(),vp.end());
    vp.erase(unique(vp.begin(),vp.end()),vp.end());
    vir = target_seg.p1;
    sort(vp.begin(),vp.end(),comp_dist);
    rep(k,(int)vp.size()-1) {
      Point mp = ( vp[k] + vp[k+1] ) / 2.0;
      if( inPolygon(tries[i],mp,0) ) return true;
    }
  }
  return false;
}

inline bool containAnyPolygon(vector<Polygon> &polies,Point p){
  rep(i,polies.size()) if( LT(polies[i][0].x,p.x) && LT(p.x,polies[i][3].x) && LT(polies[i][0].y,p.y) && LT(p.y,polies[i][1].y) ) return true;
  return false;
}

vector<Segment> createBombLine(vector<Polygon> &tries,Point sp){
  Polygon surround(4);
  surround[0] = Point(-20000,-20000); surround[1] = Point(-20000,20000); // 制約のミスを知らないとここで落ちる
  surround[2] = Point(20000,20000);   surround[3] = Point(20000,-20000);
  vector<Segment> ret;
  rep(i,tries.size()) rep(j,tries[i].size()){
    if( sp == tries[i][j] ) continue;
    Vector e = ( tries[i][j] - sp ) / abs( tries[i][j] - sp );
    Segment line = Segment(sp,sp+e*100000);
    vector<Point> vp;
    vp.push_back(sp);
    vp.push_back(tries[i][j]);
    rep(k,4) {
      if( equals(cross(surround[k]-surround[(k+1)%4],line.p1-line.p2),0.0) ) continue;
      Segment seg = Segment(surround[k],surround[(k+1)%4]);
      if( intersectSS(line,seg) ) vp.push_back(crosspoint(line,seg));
    }

    rep(k,tries.size()) rep(l,tries[k].size()) {
      Segment seg = Segment(tries[k][l],tries[k][(l+1)%tries[k].size()]);
      if( equals(cross(seg.p1-seg.p2,line.p1-line.p2),0.0) ) continue;
      if( intersectSS(seg,line) ) vp.push_back(crosspoint(seg,line));
    }

    sort(vp.begin(),vp.end());
    vp.erase(unique(vp.begin(),vp.end()),vp.end());
    vir = sp;
    sort(vp.begin(),vp.end(),comp_dist);
    rep(k,(int)vp.size()-1){
      Segment seg = Segment(vp[k],vp[k+1]);
      Point mp = ( seg.p1 + seg.p2 ) / 2.0;
      if( containAnyPolygon(tries,mp) ) break;
      ret.push_back(seg);
    }
  }
  sort(ret.begin(),ret.end());
  ret.erase(unique(ret.begin(),ret.end()),ret.end());
  return ret;
}

void makeGraph(const vector<Point> &vp,vector<vector<int> > &G,vector<Polygon> &tries){
  int V = vp.size();
  rep(i,V){
    REP(j,i+1,V){
      if( intersect_checker(tries,Segment(vp[i],vp[j])) ) continue;
      G[i].push_back(j);
      G[j].push_back(i);
    }
  }
}

//Aliceから各点への最短距離を求める
struct Data {  
  int cur;
  double weight;
  bool operator < ( const Data& data ) const { return !equals(weight,data.weight) && weight > data.weight; }
};

void dijkstra(const vector<vector<int> > &G,vector<Point> &vp,vector<double> &mindist){
  int V = vp.size();
  int sp = -1;
  rep(i,V) if( vp[i] == A ) { sp = i; break; }
  assert( sp != -1 );
  mindist[sp] = 0;
  priority_queue<Data> Q;
  Q.push((Data){sp,0});
  while( !Q.empty() ){
    Data data = Q.top(); Q.pop();
    if( LT(mindist[data.cur],data.weight) ) continue;
    rep(i,G[data.cur].size()){
      int to = G[data.cur][i];
      if( LT(data.weight+abs(vp[data.cur]-vp[to]),mindist[to]) ) {
        mindist[to] = data.weight+abs(vp[data.cur]-vp[to]);
        Q.push((Data){to,mindist[to]});
      }
    }
  }
}

void compute(){
  vector<Polygon> tries;
  rep(i,N) {
    Polygon poly;
    poly.push_back(ps[i][0]);
    poly.push_back(Point(ps[i][0].x,ps[i][1].y));
    poly.push_back(ps[i][1]);
    poly.push_back(Point(ps[i][1].x,ps[i][0].y));
    tries.push_back(poly);
  }

  if( !intersect_checker(tries,Segment(A,B)) ) { puts("0.000"); return; } 

  vector<Segment> segs = createBombLine(tries,B);

  vector<Point> vp;
  vp.push_back(A);
  rep(i,tries.size()) rep(j,tries[i].size()) vp.push_back(tries[i][j]);
  rep(i,segs.size()) rep(j,tries.size()) rep(k,tries[j].size()) {
    if( equals(cross(segs[i].p1-segs[i].p2,tries[j][k]-tries[j][(k+1)%tries[j].size()]),0.0) ) continue;
    Segment seg = Segment(tries[j][k],tries[j][(k+1)%tries[j].size()]);
    if( intersectSS(segs[i],seg) ) vp.push_back(crosspoint(segs[i],seg));
  }
  
  sort(vp.begin(),vp.end());
  vp.erase(unique(vp.begin(),vp.end()),vp.end());
  
  int V = vp.size();
  vector<vector<int> > G(V,vector<int>());
  makeGraph(vp,G,tries);

  vector<double> mindist(V,DINF);
  dijkstra(G,vp,mindist);

  double answer = DINF;
  rep(i,vp.size()) {
    if( LTE(answer,mindist[i]) ) continue;
    rep(j,segs.size()){
      double dist = mindist[i] + distanceSP(segs[j],vp[i]);
      if( LTE(answer,dist) ) continue;
      Point np = nearest_point(segs[j],vp[i]);
      Segment seg = Segment(vp[i],np);
      if( intersect_checker(tries,seg) ) continue;
      answer = dist;
    }
  }
  printf("%.6lf\n",answer);
}

int main(){
  while( scanf("%d",&N), N ){
    rep(i,N) rep(j,2) scanf("%lf %lf",&ps[i][j].x,&ps[i][j].y);
    scanf("%lf %lf %lf %lf",&A.x,&A.y,&B.x,&B.y);
    compute();
  }
  return 0;
}