#define MOD_TYPE 1

#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
// #include <atcoder/lazysegtree>
// #include <atcoder/modint>
// #include <atcoder/segtree>
using namespace atcoder;
#if 0
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
using Int = boost::multiprecision::cpp_int;
using lld = boost::multiprecision::cpp_dec_float_100;
#endif
#if 0
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>
using namespace __gnu_pbds;
using namespace __gnu_cxx;
template <typename T>
using extset =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#endif
#if 0
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#pragma region Macros
using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pld = pair<ld, ld>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;
#if MOD_TYPE == 1
constexpr ll MOD = ll(1e9 + 7);
#else
#if MOD_TYPE == 2
constexpr ll MOD = 998244353;
#else
constexpr ll MOD = 1000003;
#endif
#endif
using mint = static_modint<MOD>;
constexpr int INF = (int)1e9 + 10;
constexpr ll LINF = (ll)4e18;
const double PI = acos(-1.0);
constexpr ld EPS = 1e-10;
constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0};
constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0};
#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define REPI(i, m, n) for (int i = m; i < (int)(n); ++i)
#define repi(i, n) REPI(i, 0, n)
#define RREP(i, m, n) for (ll i = n - 1; i >= m; i--)
#define rrep(i, n) RREP(i, 0, n)
#define YES(n) cout << ((n) ? "YES" : "NO") << "\n"
#define Yes(n) cout << ((n) ? "Yes" : "No") << "\n"
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << "\n";
#define UNIQUE(v) v.erase(unique(all(v)), v.end())
struct io_init {
  io_init() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << setprecision(20) << setiosflags(ios::fixed);
  };
} io_init;
template <typename T>
inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
inline ll floor(ll a, ll b) {
  if (b < 0) a *= -1, b *= -1;
  if (a >= 0) return a / b;
  return -((-a + b - 1) / b);
}
inline ll ceil(ll a, ll b) { return floor(a + b - 1, b); }
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T &val) {
  fill((T *)array, (T *)(array + N), val);
}
template <typename T>
vector<T> compress(vector<T> &v) {
  vector<T> val = v;
  sort(all(val)), val.erase(unique(all(val)), val.end());
  for (auto &&vi : v) vi = lower_bound(all(val), vi) - val.begin();
  return val;
}
template <typename T, typename U>
constexpr istream &operator>>(istream &is, pair<T, U> &p) noexcept {
  is >> p.first >> p.second;
  return is;
}
template <typename T, typename U>
constexpr ostream &operator<<(ostream &os, pair<T, U> p) noexcept {
  os << p.first << " " << p.second;
  return os;
}
ostream &operator<<(ostream &os, mint m) {
  os << m.val();
  return os;
}
ostream &operator<<(ostream &os, modint m) {
  os << m.val();
  return os;
}
template <typename T>
constexpr istream &operator>>(istream &is, vector<T> &v) noexcept {
  for (int i = 0; i < v.size(); i++) is >> v[i];
  return is;
}
template <typename T>
constexpr ostream &operator<<(ostream &os, vector<T> &v) noexcept {
  for (int i = 0; i < v.size(); i++)
    os << v[i] << (i + 1 == v.size() ? "" : " ");
  return os;
}
template <typename T>
constexpr void operator--(vector<T> &v, int) noexcept {
  for (int i = 0; i < v.size(); i++) v[i]--;
}
random_device seed_gen;
mt19937_64 engine(seed_gen());
inline ll randInt(ll l, ll r) { return engine() % (r - l + 1) + l; }
struct BiCoef {
  vector<mint> fact_, inv_, finv_;
  BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
    fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
    for (int i = 2; i < n; i++) {
      fact_[i] = fact_[i - 1] * i;
      inv_[i] = -inv_[MOD % i] * (MOD / i);
      finv_[i] = finv_[i - 1] * inv_[i];
    }
  }
  mint C(ll n, ll k) const noexcept {
    if (n < k || n < 0 || k < 0) return 0;
    return fact_[n] * finv_[k] * finv_[n - k];
  }
  mint P(ll n, ll k) const noexcept { return C(n, k) * fact_[k]; }
  mint H(ll n, ll k) const noexcept { return C(n + k - 1, k); }
  mint Ch1(ll n, ll k) const noexcept {
    if (n < 0 || k < 0) return 0;
    mint res = 0;
    for (int i = 0; i < n; i++)
      res += C(n, i) * mint(n - i).pow(k) * (i & 1 ? -1 : 1);
    return res;
  }
  mint fact(ll n) const noexcept {
    if (n < 0) return 0;
    return fact_[n];
  }
  mint inv(ll n) const noexcept {
    if (n < 0) return 0;
    return inv_[n];
  }
  mint finv(ll n) const noexcept {
    if (n < 0) return 0;
    return finv_[n];
  }
};
BiCoef bc(200010);
#pragma endregion

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

#pragma region Geometry

using Real = long double;
using Point = complex<Real>;

inline bool eq(Real a, Real b) { return fabs(b - a) < EPS; }
inline bool eq(Point a, Point b) { return fabs(b - a) < EPS; }

Point operator*(const Point &p, const Real &d) {
  return Point(real(p) * d, imag(p) * d);
}

istream &operator>>(istream &is, Point &p) {
  Real a, b;
  is >> a >> b;
  p = Point(a, b);
  return is;
}

ostream &operator<<(ostream &os, Point &p) {
  return os << fixed << setprecision(20) << p.real() << " " << p.imag();
}

// 点 p を原点を中心として反時計回りに theta 回転
inline Point rotate(const Point &p, Real theta) {
  return Point(cos(theta) * p.real() - sin(theta) * p.imag(),
               sin(theta) * p.real() + cos(theta) * p.imag());
}

// 点 p を点 c を中心として反時計回りに theta 回転
inline Point rotate(Point p, Real theta, const Point &c) {
  p -= c;
  return rotate(p, theta) + c;
}

Real radian_to_degree(Real r) { return (r * 180.0 / PI); }

Real degree_to_radian(Real d) { return (d * PI / 180.0); }

// a-b-c の角度のうち小さい方を返す
Real get_angle(Point a, Point b, Point c) {
  a -= b, c -= b;
  Real alpha = atan2(a.imag(), a.real()), beta = atan2(c.imag(), c.real());
  if (alpha > beta) swap(alpha, beta);
  Real theta = (beta - alpha);
  return min(theta, 2 * acos(-1) - theta);
}

// a-b-c の角度（[0,2π)、a を反時計回りに回転させてcに重ねる角度）
Real get_angle2(Point a, Point b, Point c) {
  a -= b, c -= b;
  Real theta = atan2(imag(c), real(c)) - atan2(imag(a), real(a));
  while (theta < 0) theta += PI * 2;
  while (theta > PI * 2) theta -= PI * 2;
  return theta;
}

// a-b-c の角度（[0,2π)、p を間に含む方）
Real get_angle2(const Point &a, const Point &b, const Point &c,
                const Point &p) {
  if (get_angle2(a, b, p) + get_angle2(p, b, c) < PI * 2)
    return get_angle2(a, b, c);
  else
    return get_angle2(c, b, a);
}

namespace std {
bool operator<(const Point &a, const Point &b) {
  return !eq(a.real(), b.real()) ? a.real() < b.real() : a.imag() < b.imag();
}
}  // namespace std

struct Line {
  Point a, b;
  Line() = default;
  Line(Point a, Point b) : a(a), b(b) {}
  Line(Real A, Real B, Real C)  // Ax + By = C
  {
    if (eq(A, 0))
      a = Point(0, C / B), b = Point(1, C / B);
    else if (eq(B, 0))
      b = Point(C / A, 0), b = Point(C / A, 1);
    else
      a = Point(0, C / B), b = Point(C / A, 0);
  }

  friend ostream &operator<<(ostream &os, Line &p) {
    return os << p.a << " to " << p.b;
  }

  friend istream &operator>>(istream &is, Line &a) { return is >> a.a >> a.b; }
};

// Ax + By = C
tuple<Real, Real, Real> parameter(const Line &l) {
  Real A = imag(l.b) - imag(l.a);
  Real B = real(l.a) - real(l.b);
  Real C = real(l.a) * A + imag(l.a) * B;
  return {A, B, C};
}

struct Segment : Line {
  Segment() = default;
  Segment(Point a, Point b) : Line(a, b) {}
};

struct Circle {
  Point p;
  Real r;
  Circle() = default;
  Circle(Point p, Real r) : p(p), r(r) {}
};

using Points = vector<Point>;
using Polygon = vector<Point>;
using Segments = vector<Segment>;
using Lines = vector<Line>;
using Circles = vector<Circle>;

inline Real cross(const Point &a, const Point &b) {
  return real(a) * imag(b) - imag(a) * real(b);
}

inline Real dot(const Point &a, const Point &b) {
  return real(a) * real(b) + imag(a) * imag(b);
}

// 直線がx軸となす角 [0, π)
// to do: verify
inline Real get_angle(const Line &l) {
  Point p = l.a - l.b;
  if (imag(p) < 0) p *= -1;
  return get_angle2(Point(1, 0), Point(0, 0), p);
}

// 2直線がなす角 [0, π/2]
// to do: verify
inline Real get_angle(const Line &l1, const Line &l2) {
  Real theta = get_angle(l1) - get_angle(l2);
  if (theta < 0) theta += PI;
  return theta >= PI / 2.0 ? theta - PI / 2.0 : theta;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C
// 点の回転方向
int ccw(const Point &a, Point b, Point c) {
  b = b - a, c = c - a;
  if (cross(b, c) > EPS) return +1;   // "COUNTER_CLOCKWISE"
  if (cross(b, c) < -EPS) return -1;  // "CLOCKWISE"
  if (dot(b, c) < 0) return +2;       // "ONLINE_BACK"
  if (norm(b) < norm(c)) return -2;   // "ONLINE_FRONT"
  return 0;                           // "ON_SEGMENT"
}

// p, q を m : n に内分する点
inline Point internal_point(const Point &p, const Point &q, Real m, Real n) {
  return (n * p + m * q) / (m + n);
}

// p, q を m : n に外分する点
inline Point external_point(const Point &p, const Point &q, Real m, Real n) {
  return internal_point(p, q, m, -n);
}

// 垂直ベクトル
inline Point orthvector(const Point p) { return Point(imag(p), -real(p)); }

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
// 平行判定
inline bool parallel(const Line &a, const Line &b) {
  return eq(cross(a.b - a.a, b.b - b.a), 0.0);
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
// 垂直判定
inline bool orthogonal(const Line &a, const Line &b) {
  return eq(dot(a.a - a.b, b.a - b.b), 0.0);
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A
// 射影
// 直線 l に p から垂線を引いた交点を求める
inline Point projection(const Line &l, const Point &p) {
  double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}

inline Point projection(const Segment &l, const Point &p) {
  double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B
// 反射
// 直線 l を対称軸として点 p と線対称にある点を求める
inline Point reflection(const Line &l, const Point &p) {
  return p + (projection(l, p) - p) * 2.0;
}

// 点 p を通り直線 l に垂直な直線
inline Line verticalline(const Line &l, const Point &p) {
  return Line(p, p + orthvector(l.a - l.b));
}

// 点 p, q の垂直二等分線
inline Line bisector(const Point &p, const Point &q) {
  Line l(p, q);
  Point m = internal_point(p, q, 1, 1);
  return verticalline(l, m);
}
inline Line bisector(const Segment &sg) { return bisector(sg.a, sg.b); }

inline bool intersect(const Line &l, const Point &p) {
  return abs(ccw(l.a, l.b, p)) != 1;
}

inline bool intersect(const Line &l, const Line &m) {
  return abs(cross(l.b - l.a, m.b - m.a)) > EPS ||
         abs(cross(l.b - l.a, m.b - l.a)) < EPS;
}

inline bool intersect(const Segment &s, const Point &p) {
  return ccw(s.a, s.b, p) == 0;
}

inline bool intersect(const Line &l, const Segment &s) {
  return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;
}

inline Real distance(const Line &l, const Point &p);

inline bool intersect(const Circle &c, const Line &l) {
  return distance(l, c.p) <= c.r + EPS;
}

inline bool intersect(const Circle &c, const Point &p) {
  return abs(abs(p - c.p) - c.r) < EPS;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B
bool intersect(const Segment &s, const Segment &t) {
  return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
         ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

int intersect(const Circle &c, const Segment &l) {
  if (norm(projection(l, c.p) - c.p) - c.r * c.r > EPS) return 0;
  auto d1 = abs(c.p - l.a), d2 = abs(c.p - l.b);
  if (d1 < c.r + EPS && d2 < c.r + EPS) return 0;
  if (d1 < c.r - EPS && d2 > c.r + EPS || d1 > c.r + EPS && d2 < c.r - EPS)
    return 1;
  const Point h = projection(l, c.p);
  if (dot(l.a - h, l.b - h) < 0) return 2;
  return 0;
}

// 共通接戦の本数
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_A&lang=jp
int intersect(Circle c1, Circle c2) {
  if (c1.r < c2.r) swap(c1, c2);
  Real d = abs(c1.p - c2.p);
  if (c1.r + c2.r < d) return 4;
  if (eq(c1.r + c2.r, d)) return 3;
  if (c1.r - c2.r < d) return 2;
  if (eq(c1.r - c2.r, d)) return 1;
  return 0;
}

inline Real distance(const Point &a, const Point &b) { return abs(a - b); }

inline Real distance(const Line &l, const Point &p) {
  return abs(p - projection(l, p));
}

inline Real distance(const Line &l, const Line &m) {
  return intersect(l, m) ? 0 : distance(l, m.a);
}

inline Real distance(const Segment &s, const Point &p) {
  Point r = projection(s, p);
  if (intersect(s, r)) return abs(r - p);
  return min(abs(s.a - p), abs(s.b - p));
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D
Real distance(const Segment &a, const Segment &b) {
  if (intersect(a, b)) return 0;
  return min(
      {distance(a, b.a), distance(a, b.b), distance(b, a.a), distance(b, a.b)});
}

Real distance(const Line &l, const Segment &s) {
  if (intersect(l, s)) return 0;
  return min(distance(l, s.a), distance(l, s.b));
}

Point crosspoint(const Line &l, const Line &m) {
  Real A = cross(l.b - l.a, m.b - m.a);
  Real B = cross(l.b - l.a, l.b - m.a);
  if (eq(abs(A), 0.0) && eq(abs(B), 0.0)) return m.a;
  return m.a + (m.b - m.a) * B / A;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_C
Point crosspoint(const Segment &l, const Segment &m) {
  return crosspoint(Line(l), Line(m));
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D
pair<Point, Point> crosspoint(const Circle &c, const Line l) {
  Point pr = projection(l, c.p);
  Point e = (l.b - l.a) / abs(l.b - l.a);
  if (eq(distance(l, c.p), c.r)) return {pr, pr};
  double base = sqrt(c.r * c.r - norm(pr - c.p));
  return {pr - e * base, pr + e * base};
}

pair<Point, Point> crosspoint(const Circle &c, const Segment &l) {
  Line aa = Line(l.a, l.b);
  if (intersect(c, l) == 2) return crosspoint(c, aa);
  auto ret = crosspoint(c, aa);
  if (dot(l.a - ret.first, l.b - ret.first) < 0)
    ret.second = ret.first;
  else
    ret.first = ret.second;
  return ret;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_E
pair<Point, Point> crosspoint(const Circle &c1, const Circle &c2) {
  Real d = abs(c1.p - c2.p);
  Real a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  Real t = atan2(c2.p.imag() - c1.p.imag(), c2.p.real() - c1.p.real());
  Point p1 = c1.p + Point(cos(t + a) * c1.r, sin(t + a) * c1.r);
  Point p2 = c1.p + Point(cos(t - a) * c1.r, sin(t - a) * c1.r);
  return {p1, p2};
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_F
// 点 p を通る円 c の接線（接点を返す）
pair<Point, Point> tangent(const Circle &c1, const Point &p2) {
  return crosspoint(c1, Circle(p2, sqrt(norm(c1.p - p2) - c1.r * c1.r)));
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_G
// 円 c1, c2 の共通接線
Lines tangent(Circle c1, Circle c2) {
  Lines ret;
  if (c1.r < c2.r) swap(c1, c2);
  Real g = norm(c1.p - c2.p);
  if (eq(g, 0)) return ret;
  Point u = (c2.p - c1.p) / sqrt(g);
  Point v = rotate(u, PI * 0.5);
  for (int s : {-1, 1}) {
    Real h = (c1.r + s * c2.r) / sqrt(g);
    if (eq(1 - h * h, 0)) {
      ret.emplace_back(c1.p + u * c1.r, c1.p + (u + v) * c1.r);
    } else if (1 - h * h > 0) {
      Point uu = u * h, vv = v * sqrt(1 - h * h);
      ret.emplace_back(c1.p + (uu + vv) * c1.r, c2.p - (uu + vv) * c2.r * s);
      ret.emplace_back(c1.p + (uu - vv) * c1.r, c2.p - (uu - vv) * c2.r * s);
    }
  }
  return ret;
}

// 2点 p, q からの距離が m : n (m != n)となる点の軌跡
Circle Apollonius(const Point &p, const Point &q, Real m, Real n) {
  assert(!eq(m, n));
  Circle res;
  res.p = external_point(p, q, m * m, n * n);
  res.r = sqrt(fabs(p - res.p) * fabs(q - res.p));
  Point pp = res.p + Point(res.r, 0);
  assert(eq(distance(pp, p) * n, distance(pp, q) * m));
  return res;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B
// 凸性判定
bool is_convex(const Polygon &p) {
  int n = (int)p.size();
  for (int i = 0; i < n; i++) {
    if (ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]) == -1) return false;
  }
  return true;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A
// 凸包
Polygon convex_hull(Polygon &p, bool strict = true) {
  int n = (int)p.size(), k = 0;
  if (n <= 2) return p;
  sort(p.begin(), p.end());
  vector<Point> ch(2 * n);
  Real EPS2 = (strict ? EPS : -EPS);
  for (int i = 0; i < n; ch[k++] = p[i++]) {
    while (k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS2) --k;
  }
  for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
    while (k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS2) --k;
  }
  ch.resize(k - 1);
  return ch;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C
// 多角形と点の包含判定
enum { OUT, ON, IN };

int contains(const Polygon &Q, const Point &p) {
  bool in = false;
  for (int i = 0; i < Q.size(); i++) {
    Point a = Q[i] - p, b = Q[(i + 1) % Q.size()] - p;
    if (a.imag() > b.imag()) swap(a, b);
    if (a.imag() <= 0 && 0 < b.imag() && cross(a, b) < 0) in = !in;
    if (cross(a, b) == 0 && dot(a, b) <= 0) return ON;
  }
  return in ? IN : OUT;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1033
// 線分の重複除去
void merge_segments(vector<Segment> &segs) {
  auto merge_if_able = [](Segment &s1, const Segment &s2) {
    if (abs(cross(s1.b - s1.a, s2.b - s2.a)) > EPS) return false;
    if (ccw(s1.a, s2.a, s1.b) == 1 || ccw(s1.a, s2.a, s1.b) == -1) return false;
    if (ccw(s1.a, s1.b, s2.a) == -2 || ccw(s2.a, s2.b, s1.a) == -2)
      return false;
    s1 = Segment(min(s1.a, s2.a), max(s1.b, s2.b));
    return true;
  };

  for (int i = 0; i < segs.size(); i++) {
    if (segs[i].b < segs[i].a) swap(segs[i].a, segs[i].b);
  }
  for (int i = 0; i < segs.size(); i++) {
    for (int j = i + 1; j < segs.size(); j++) {
      if (merge_if_able(segs[i], segs[j])) {
        segs[j--] = segs.back(), segs.pop_back();
      }
    }
  }
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1033
// 線分アレンジメント
// 任意の2線分の交点を頂点としたグラフを構築する
vector<vector<int>> segment_arrangement(vector<Segment> &segs,
                                        vector<Point> &ps) {
  vector<vector<int>> g;
  int N = (int)segs.size();
  for (int i = 0; i < N; i++) {
    ps.emplace_back(segs[i].a);
    ps.emplace_back(segs[i].b);
    for (int j = i + 1; j < N; j++) {
      const Point p1 = segs[i].b - segs[i].a;
      const Point p2 = segs[j].b - segs[j].a;
      if (cross(p1, p2) == 0) continue;
      if (intersect(segs[i], segs[j])) {
        ps.emplace_back(crosspoint(segs[i], segs[j]));
      }
    }
  }
  sort(begin(ps), end(ps));
  ps.erase(unique(begin(ps), end(ps)), end(ps));

  int M = (int)ps.size();
  g.resize(M);
  for (int i = 0; i < N; i++) {
    vector<int> vec;
    for (int j = 0; j < M; j++) {
      if (intersect(segs[i], ps[j])) {
        vec.emplace_back(j);
      }
    }
    for (int j = 1; j < vec.size(); j++) {
      g[vec[j - 1]].push_back(vec[j]);
      g[vec[j]].push_back(vec[j - 1]);
    }
  }
  return (g);
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_C
// 凸多角形の切断
// 直線 l.a-l.b で切断しその左側にできる凸多角形を返す
Polygon convex_cut(const Polygon &U, Line l) {
  Polygon ret;
  for (int i = 0; i < U.size(); i++) {
    Point now = U[i], nxt = U[(i + 1) % U.size()];
    if (ccw(l.a, l.b, now) != -1) ret.push_back(now);
    if (ccw(l.a, l.b, now) * ccw(l.a, l.b, nxt) < 0) {
      ret.push_back(crosspoint(Line(now, nxt), l));
    }
  }
  return (ret);
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A
// 多角形の面積
Real area(const Polygon &p) {
  Real A = 0;
  for (int i = 0; i < p.size(); ++i) {
    A += cross(p[i], p[(i + 1) % p.size()]);
  }
  return A * 0.5;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H
// 円と多角形の共通部分の面積
Real area(const Polygon &p, const Circle &c) {
  if (p.size() < 3) return 0.0;
  function<Real(Circle, Point, Point)> cross_area =
      [&](const Circle &c, const Point &a, const Point &b) {
        Point va = c.p - a, vb = c.p - b;
        Real f = cross(va, vb), ret = 0.0;
        if (eq(f, 0.0)) return ret;
        if (max(abs(va), abs(vb)) < c.r + EPS) return f;
        if (distance(Segment(a, b), c.p) > c.r - EPS)
          return c.r * c.r * arg(vb * conj(va));
        auto u = crosspoint(c, Segment(a, b));
        vector<Point> tot{a, u.first, u.second, b};
        for (int i = 0; i + 1 < tot.size(); i++) {
          ret += cross_area(c, tot[i], tot[i + 1]);
        }
        return ret;
      };
  Real A = 0;
  for (int i = 0; i < p.size(); i++) {
    A += cross_area(c, p[i], p[(i + 1) % p.size()]);
  }
  return A / 2.0;
}

// 2円の共通部分の面積
Real area(const Circle &c1, const Circle &c2) {
  int t = intersect(c1, c2);
  if (t > 2) return 0.0;
  if (t < 2) return min(c1.r * c1.r * PI, c2.r * c2.r * PI);
  Real res = 0.0;
  auto [p1, p2] = crosspoint(c1, c2);
  Real theta1 = get_angle2(p1, c1.p, p2, c2.p);
  res += c1.r * c1.r * 0.5 * (theta1 - sin(theta1));
  Real theta2 = get_angle2(p2, c2.p, p1, c1.p);
  res += c2.r * c2.r * 0.5 * (theta2 - sin(theta2));
  return fabs(res);
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_B
// 凸多角形の直径(最遠頂点対間距離)
Real convex_diameter(const Polygon &p) {
  int N = (int)p.size();
  int is = 0, js = 0;
  for (int i = 1; i < N; i++) {
    if (p[i].imag() > p[is].imag()) is = i;
    if (p[i].imag() < p[js].imag()) js = i;
  }
  Real maxdis = norm(p[is] - p[js]);

  int maxi, maxj, i, j;
  i = maxi = is;
  j = maxj = js;
  do {
    if (cross(p[(i + 1) % N] - p[i], p[(j + 1) % N] - p[j]) >= 0) {
      j = (j + 1) % N;
    } else {
      i = (i + 1) % N;
    }
    if (norm(p[i] - p[j]) > maxdis) {
      maxdis = norm(p[i] - p[j]);
      maxi = i;
      maxj = j;
    }
  } while (i != is || j != js);
  return sqrt(maxdis);
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_5_A
// 最近点対
Real closest_pair(Points ps) {
  if (ps.size() <= 1) throw(0);
  sort(begin(ps), end(ps));

  auto compare_y = [&](const Point &a, const Point &b) {
    return imag(a) < imag(b);
  };
  vector<Point> beet(ps.size());
  const Real INF = 1e18;

  function<Real(int, int)> rec = [&](int left, int right) {
    if (right - left <= 1) return INF;
    int mid = (left + right) >> 1;
    auto x = real(ps[mid]);
    auto ret = min(rec(left, mid), rec(mid, right));
    inplace_merge(begin(ps) + left, begin(ps) + mid, begin(ps) + right,
                  compare_y);
    int ptr = 0;
    for (int i = left; i < right; i++) {
      if (abs(real(ps[i]) - x) >= ret) continue;
      for (int j = 0; j < ptr; j++) {
        auto luz = ps[i] - beet[ptr - j - 1];
        if (imag(luz) >= ret) break;
        ret = min(ret, abs(luz));
      }
      beet[ptr++] = ps[i];
    }
    return ret;
  };
  return rec(0, (int)ps.size());
}

// 凸多角形の共通部分
Polygon intersection(const Polygon &p1, const Polygon &p2) {
  int n1 = p1.size(), n2 = p2.size();
  Polygon res;
  rep(i, n1) {
    if (contains(p2, p1[i]) != OUT) res.push_back(p1[i]);
  }
  rep(i, n2) {
    if (contains(p1, p2[i]) != OUT) res.push_back(p2[i]);
  }
  rep(i, n1) rep(j, n2) {
    Segment s1(p1[i], p1[(i + 1) % n1]);
    Segment s2(p2[j], p2[(j + 1) % n2]);
    if (intersect(s1, s2)) res.push_back(crosspoint(s1, s2));
  }
  return convex_hull(res);
}

#pragma endregion

void solve() {
  int n, m;
  cin >> n >> m;

  vector<double> x(n * 2), y(n * 2);
  vector<Segment> s(n);
  rep(i, n) {
    cin >> x[i * 2] >> y[i * 2] >> x[i * 2 + 1] >> y[i * 2 + 1];
    s[i] = Segment({x[i * 2], y[i * 2]}, {x[i * 2 + 1], y[i * 2 + 1]});
  }

  auto can = [&](int i, int type1, int j, int type2) {
    int num1 = i * 2 + type1;
    int num2 = j * 2 + type2;
    Point p(x[num1], y[num1]);
    Point q(x[num2], y[num2]);
    Segment pq(p, q);
    rep(k, n) {
      if (k == i or k == j) continue;
      if (intersect(pq, s[k])) return false;
    }
    return true;
  };

  double d[300][300];
  rep(i, n * 2) rep(j, n * 2) d[i][j] = (i == j ? 0.0 : 1e18);

  rep(i, n) REP(j, i, n) rep(t1, 2) rep(t2, 2) {
    if (can(i, t1, j, t2)) {
      int num1 = i * 2 + t1;
      int num2 = j * 2 + t2;
      d[num1][num2] = d[num2][num1] =
          distance(Point(x[num1], y[num1]), Point(x[num2], y[num2]));
    }
  }

  rep(k, n * 2) rep(i, n * 2) rep(j, n * 2) {
    chmin(d[i][j], d[i][k] + d[k][j]);
  }
  rep(_, m) {
    int i, j, type1, type2;
    cin >> i >> type1 >> j >> type2;
    i--, j--;
    type1--, type2--;
    int num1 = i * 2 + type1;
    int num2 = j * 2 + type2;
    cout << d[num1][num2] << "\n";
  }
}

int main() { solve(); }