Problem p01285 (C++) — buggy submission, verdict: Runtime Error

#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-6)
#define equals(a, b) (fabs((a) - (b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

class Point {
public:
  double x, y;

  Point(double x = 0, double y = 0) : x(x), y(y) {}

  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(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*(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;
  int index;
  Segment(Point p1 = Point(), Point p2 = Point(), int index = -1)
      : p1(p1), p2(p2), index(index) {}
  bool operator<(const Segment &s) const {
    return (p2 == s.p2) ? p1 < s.p1 : p2 < s.p2;
  }
  bool operator==(const Segment &s) const {
    return (s.p1 == p1 && s.p2 == p2) || (s.p1 == p2 && s.p2 == p1);
  }
};

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

ostream &operator<<(ostream &os, const Point &a) {
  os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  os << "( " << a.p1 << " , " << a.p2 << " )";
}

double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }

double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }

double norm(Point a) { return a.x * a.x + a.y * a.y; }

double abs(Point a) { return sqrt(norm(a)); }

// rad ??????§?????????????????¢???????§???????????????????¨
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// ????????????????¢????????????
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev ?????? cur ??????????£??? next ??????????????????§??????????±???????
double getArg(Point a, Point b, Point c) {
  double arg1 = atan2(b.y - a.y, b.x - a.x);
  double arg2 = atan2(c.y - b.y, c.x - b.x);
  double arg = fabs(arg1 - arg2);
  while (arg > M_PI)
    arg -= 2.0 * M_PI;
  return fabs(arg);
}

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 intersectLL(Line l, Line m) {
  return abs(cross(l.p2 - l.p1, m.p2 - m.p1)) > EPS || // non-parallel
         abs(cross(l.p2 - l.p1, m.p1 - l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2 - l.p1, s.p1 - l.p1) * // s[0] is left of l
             cross(l.p2 - l.p1, s.p2 - l.p1) <
         EPS; // s[1] is right of l
}
bool intersectLP(Line l, Point p) {
  return abs(cross(l.p2 - p, l.p1 - p)) < EPS;
}
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 distanceLP(Line l, Point p) { return abs(p - projection(l, p)); }
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s))
    return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
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));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t))
    return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.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]); //?????????????°??????????????????
    return vec[1];
    // return m.p1;
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}

// cross product of pq and pr
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);
}

// returns true if point r is on the same line as the line pq
bool collinear(Point p, Point q, Point r) {
  return fabs(cross3p(p, q, r)) < EPS;
}

// returns true if point t is on the left side of line pq
bool ccwtest(Point p, Point q, Point r) {
  return cross3p(p, q, r) > 0; // can be modified to accept collinear points
}

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)));
}

// ------------------

double heron(Point A, Point B, Point C) {
  double a = abs(B - C);
  double b = abs(A - C);
  double c = abs(A - B);
  double s = (a + b + c) / 2;
  return sqrt(s * (s - a) * (s - b) * (s - c));
}

Line calcLine(Line line1, Line line2, Point p1, Point p2) {
  Point cp = crosspoint(line1, line2);
  double S = heron(p1, cp, p2);
  double a = abs(p1 - cp);
  double b = abs(p2 - cp);
  double arg_a = asin((2.0 * S) / (a * b));
  if (equals(2 * S, a * b))
    arg_a = toRad(90);
  // arg_a = getArg(p1,cp,p2);

  // assert( !( cp == p1 || cp == p2 || p1 == p2 ) );

  int res = ccw(cp, p1, p2);
  // assert( ( res == CLOCKWISE || res == COUNTER_CLOCKWISE ));
  // while( !( res == CLOCKWISE || res == COUNTER_CLOCKWISE ));
  Point base;
  if (res == COUNTER_CLOCKWISE)
    base = p1;
  else
    base = p2;
  Point not_base = (base == p1) ? p2 : p1;
  // cout << base << " -> " << cp << " -> " << not_base << endl;
  arg_a = (toRad(180.0) - getArg(base, cp, not_base));
  // puts("^^^^^");
  // cout << "base = " << base << " | " << (arg_a*180/M_PI)<< endl;
  // cout << line1 << " and " << line2 << endl;
  // cout << cp << " | " << p1 << " | " << p2 << endl;

  Vector e = (base - cp) / abs(base - cp);
  e = rotate(e, arg_a / 2.0);
  Line tmp = Line(cp, cp + e * 100);
  // cout << "return = " << tmp << endl;
  // puts("_____");
  return tmp;
}

const string MANY = "Many";
const string NONE = "None";
#define all(x) (x.begin(), x.end())
void compute(vector<Line> &vec) {

  if (vec.size() <= 2) {
    cout << MANY << endl;
    return;
  }

  vector<Line> candidateLines;
  int n = vec.size();
  rep(i, n) REP(j, i + 1, n) {
    if (equals(cross(vec[i].p1 - vec[i].p2, vec[j].p1 - vec[j].p2), 0.0)) {
      Vector e = (vec[i].p2 - vec[i].p1) / abs(vec[i].p2 - vec[i].p1);
      e = rotate(e, toRad(90));
      Line line = Line(vec[i].p1, vec[i].p1 + e * 100);
      Point cp1 = crosspoint(line, vec[i]);
      Point cp2 = crosspoint(line, vec[j]);
      Point mp = (cp1 + cp2) / 2.0;
      e = (vec[i].p2 - vec[i].p1) / abs(vec[i].p2 - vec[i].p1);
      line = Line(mp, mp + e * 100);
      line.index = candidateLines.size();
      candidateLines.push_back(line);
    } else {
      // cout << vec[i] << " x " << vec[j] << endl;
      Point cp = crosspoint(vec[i], vec[j]);
      Point I = (vec[i].p1 == cp) ? vec[i].p2 : vec[i].p1;
      Point J = (vec[j].p1 == cp) ? vec[j].p2 : vec[j].p1;
      Vector e1 = (I - cp) / abs(I - cp);
      Vector e2 = (J - cp) / abs(J - cp);
      Line tmp = calcLine(vec[i], vec[j], cp + e1 * 100, cp + e2 * 100);
      // cout << "tmp = " << tmp << endl;
      int Index = candidateLines.size();
      tmp.index = Index;
      candidateLines.push_back(tmp);
      tmp = calcLine(vec[i], vec[j], cp + e1 * 100, cp - e2 * 100);
      // cout << "tmp = " << tmp << endl;
      tmp.index = Index;
      candidateLines.push_back(tmp);
    }
    if (candidateLines.size() >= 50)
      break;
  }

  vector<Point> candidatePoints;

  rep(i, candidateLines.size()) REP(j, i + 1, candidateLines.size()) {
    Line line1 = candidateLines[i];
    Line line2 = candidateLines[j];
    if (equals(cross(line1.p1 - line1.p2, line2.p1 - line2.p2), 0.0))
      continue;
    Point cp = crosspoint(line1, line2);
    candidatePoints.push_back(cp);
  }

  vector<Point> &v = candidatePoints;
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());

  vector<Point> answer;
  rep(i, candidatePoints.size()) {
    Point p = candidatePoints[i];
    // puts("");
    // cout << "p = " << p << endl;
    double dist = -1;
    bool success = true;
    rep(j, vec.size()) {
      double tmp = distanceLP(vec[j], p);
      if (equals(dist, -1))
        dist = tmp;
      else if (!equals(dist, tmp)) {
        success = false; /*break;*/
      }
      // cout << dist << " ?? " << tmp << endl;
    }
    // cout << "success ?= " << success << endl;
    if (success)
      answer.push_back(p);
    if (answer.size() >= 2)
      break;
  }

  if (answer.size() == 1)
    printf("%.10f %.10f\\n", answer[0].x, answer[0].y);
  else if (answer.empty())
    cout << NONE << endl;
  else
    cout << MANY << endl;
}

int main() {
  /*
  Point p = Point(0,1);
  cout << rotate(p,toRad(90)) << endl;
  */
  int n;
  while (cin >> n, n) {
    vector<Line> vec(n);
    rep(i, n) cin >> vec[i].p1.x >> vec[i].p1.y >> vec[i].p2.x >> vec[i].p2.y;
    compute(vec);
  }
  return 0;
}

Error: WA

Fixed submission:

#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-6)
#define equals(a, b) (fabs((a) - (b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

class Point {
public:
  double x, y;

  Point(double x = 0, double y = 0) : x(x), y(y) {}

  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(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*(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;
  int index;
  Segment(Point p1 = Point(), Point p2 = Point(), int index = -1)
      : p1(p1), p2(p2), index(index) {}
  bool operator<(const Segment &s) const {
    return (p2 == s.p2) ? p1 < s.p1 : p2 < s.p2;
  }
  bool operator==(const Segment &s) const {
    return (s.p1 == p1 && s.p2 == p2) || (s.p1 == p2 && s.p2 == p1);
  }
};

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

ostream &operator<<(ostream &os, const Point &a) {
  os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  os << "( " << a.p1 << " , " << a.p2 << " )";
}

double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }

double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }

double norm(Point a) { return a.x * a.x + a.y * a.y; }

double abs(Point a) { return sqrt(norm(a)); }

// rad ??????§?????????????????¢???????§???????????????????¨
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// ????????????????¢????????????
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev ?????? cur ??????????£??? next ??????????????????§??????????±???????
double getArg(Point a, Point b, Point c) {
  double arg1 = atan2(b.y - a.y, b.x - a.x);
  double arg2 = atan2(c.y - b.y, c.x - b.x);
  double arg = fabs(arg1 - arg2);
  while (arg > M_PI)
    arg -= 2.0 * M_PI;
  return fabs(arg);
}

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 intersectLL(Line l, Line m) {
  return abs(cross(l.p2 - l.p1, m.p2 - m.p1)) > EPS || // non-parallel
         abs(cross(l.p2 - l.p1, m.p1 - l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2 - l.p1, s.p1 - l.p1) * // s[0] is left of l
             cross(l.p2 - l.p1, s.p2 - l.p1) <
         EPS; // s[1] is right of l
}
bool intersectLP(Line l, Point p) {
  return abs(cross(l.p2 - p, l.p1 - p)) < EPS;
}
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 distanceLP(Line l, Point p) { return abs(p - projection(l, p)); }
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s))
    return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
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));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t))
    return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.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]); //?????????????°??????????????????
    return vec[1];
    // return m.p1;
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}

// cross product of pq and pr
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);
}

// returns true if point r is on the same line as the line pq
bool collinear(Point p, Point q, Point r) {
  return fabs(cross3p(p, q, r)) < EPS;
}

// returns true if point t is on the left side of line pq
bool ccwtest(Point p, Point q, Point r) {
  return cross3p(p, q, r) > 0; // can be modified to accept collinear points
}

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)));
}

// ------------------

double heron(Point A, Point B, Point C) {
  double a = abs(B - C);
  double b = abs(A - C);
  double c = abs(A - B);
  double s = (a + b + c) / 2;
  return sqrt(s * (s - a) * (s - b) * (s - c));
}

Line calcLine(Line line1, Line line2, Point p1, Point p2) {
  Point cp = crosspoint(line1, line2);
  double S = heron(p1, cp, p2);
  double a = abs(p1 - cp);
  double b = abs(p2 - cp);
  double arg_a = asin((2.0 * S) / (a * b));
  if (equals(2 * S, a * b))
    arg_a = toRad(90);
  // arg_a = getArg(p1,cp,p2);

  assert(!(cp == p1 || cp == p2 || p1 == p2));

  int res = ccw(cp, p1, p2);
  // assert( ( res == CLOCKWISE || res == COUNTER_CLOCKWISE ));
  // while( !( res == CLOCKWISE || res == COUNTER_CLOCKWISE ));
  Point base;
  if (res == COUNTER_CLOCKWISE)
    base = p1;
  else
    base = p2;
  Point not_base = (base == p1) ? p2 : p1;
  // cout << base << " -> " << cp << " -> " << not_base << endl;
  arg_a = (toRad(180.0) - getArg(base, cp, not_base));
  // puts("^^^^^");
  // cout << "base = " << base << " | " << (arg_a*180/M_PI)<< endl;
  // cout << line1 << " and " << line2 << endl;
  // cout << cp << " | " << p1 << " | " << p2 << endl;

  Vector e = (base - cp) / abs(base - cp);
  e = rotate(e, arg_a / 2.0);
  Line tmp = Line(cp, cp + e * 100);
  // cout << "return = " << tmp << endl;
  // puts("_____");
  return tmp;
}

const string MANY = "Many";
const string NONE = "None";
#define all(x) (x.begin(), x.end())
void compute(vector<Line> &vec) {

  if (vec.size() <= 2) {
    cout << MANY << endl;
    return;
  }

  vector<Line> candidateLines;
  int n = vec.size();
  rep(i, n) REP(j, i + 1, n) {
    if (equals(cross(vec[i].p1 - vec[i].p2, vec[j].p1 - vec[j].p2), 0.0)) {
      Vector e = (vec[i].p2 - vec[i].p1) / abs(vec[i].p2 - vec[i].p1);
      e = rotate(e, toRad(90));
      Line line = Line(vec[i].p1, vec[i].p1 + e * 100);
      Point cp1 = crosspoint(line, vec[i]);
      Point cp2 = crosspoint(line, vec[j]);
      Point mp = (cp1 + cp2) / 2.0;
      e = (vec[i].p2 - vec[i].p1) / abs(vec[i].p2 - vec[i].p1);
      line = Line(mp, mp + e * 100);
      line.index = candidateLines.size();
      candidateLines.push_back(line);
    } else {
      // cout << vec[i] << " x " << vec[j] << endl;
      Point cp = crosspoint(vec[i], vec[j]);
      Point I = (vec[i].p1 == cp) ? vec[i].p2 : vec[i].p1;
      Point J = (vec[j].p1 == cp) ? vec[j].p2 : vec[j].p1;
      Vector e1 = (I - cp) / abs(I - cp);
      Vector e2 = (J - cp) / abs(J - cp);
      Line tmp = calcLine(vec[i], vec[j], cp + e1 * 100, cp + e2 * 100);
      // cout << "tmp = " << tmp << endl;
      int Index = candidateLines.size();
      tmp.index = Index;
      candidateLines.push_back(tmp);
      tmp = calcLine(vec[i], vec[j], cp + e1 * 100, cp - e2 * 100);
      // cout << "tmp = " << tmp << endl;
      tmp.index = Index;
      candidateLines.push_back(tmp);
    }
    if (candidateLines.size() >= 50)
      break;
  }

  vector<Point> candidatePoints;

  rep(i, candidateLines.size()) REP(j, i + 1, candidateLines.size()) {
    Line line1 = candidateLines[i];
    Line line2 = candidateLines[j];
    if (equals(cross(line1.p1 - line1.p2, line2.p1 - line2.p2), 0.0))
      continue;
    Point cp = crosspoint(line1, line2);
    candidatePoints.push_back(cp);
  }

  vector<Point> &v = candidatePoints;
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());

  vector<Point> answer;
  rep(i, candidatePoints.size()) {
    Point p = candidatePoints[i];
    // puts("");
    // cout << "p = " << p << endl;
    double dist = -1;
    bool success = true;
    rep(j, vec.size()) {
      double tmp = distanceLP(vec[j], p);
      if (equals(dist, -1))
        dist = tmp;
      else if (!equals(dist, tmp)) {
        success = false; /*break;*/
      }
      // cout << dist << " ?? " << tmp << endl;
    }
    // cout << "success ?= " << success << endl;
    if (success)
      answer.push_back(p);
    if (answer.size() >= 2)
      break;
  }

  if (answer.size() == 1)
    printf("%.10f %.10f\\n", answer[0].x, answer[0].y);
  else if (answer.empty())
    cout << NONE << endl;
  else
    cout << MANY << endl;
}

int main() {
  /*
  Point p = Point(0,1);
  cout << rotate(p,toRad(90)) << endl;
  */
  int n;
  while (cin >> n, n) {
    vector<Line> vec(n);
    rep(i, n) cin >> vec[i].p1.x >> vec[i].p1.y >> vec[i].p2.x >> vec[i].p2.y;
    compute(vec);
  }
  return 0;
}