#include <bits/stdc++.h>

#ifdef _MSC_VER
#  include <intrin.h>
#else
#  include <x86intrin.h>
#endif

#include <limits>
#include <type_traits>

namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
    if constexpr (cond_v) {
        return std::forward<Then>(then);
    } else {
        return std::forward<OrElse>(or_else);
    }
}

// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;

template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;

// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;

// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long int> { using type = __uint128_t; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;

template <typename T, typename = void>
struct rec_value_type {
    using type = T;
};
template <typename T>
struct rec_value_type<T, std::void_t<typename T::value_type>> {
    using type = typename rec_value_type<typename T::value_type>::type;
};
template <typename T>
using rec_value_type_t = typename rec_value_type<T>::type;

} // namespace suisen

// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;

// ! macros (internal)
#define DETAIL_OVERLOAD2(_1,_2,name,...) name
#define DETAIL_OVERLOAD3(_1,_2,_3,name,...) name
#define DETAIL_OVERLOAD4(_1,_2,_3,_4,name,...) name

#define DETAIL_REP4(i,l,r,s)  for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define DETAIL_REP3(i,l,r)    DETAIL_REP4(i,l,r,1)
#define DETAIL_REP2(i,n)      DETAIL_REP3(i,0,n)
#define DETAIL_REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define DETAIL_REPINF2(i,l)   DETAIL_REPINF3(i,l,1)
#define DETAIL_REPINF1(i)     DETAIL_REPINF2(i,0)
#define DETAIL_RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define DETAIL_RREP3(i,l,r)   DETAIL_RREP4(i,l,r,1)
#define DETAIL_RREP2(i,n)     DETAIL_RREP3(i,0,n)

#define DETAIL_CAT_I(a, b) a##b
#define DETAIL_CAT(a, b) DETAIL_CAT_I(a, b)
#define DETAIL_UNIQVAR(tag) DETAIL_CAT(tag, __LINE__)

// ! macros
#define REP(...)    DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_REP4   , DETAIL_REP3   , DETAIL_REP2   )(__VA_ARGS__)
#define RREP(...)   DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_RREP4  , DETAIL_RREP3  , DETAIL_RREP2  )(__VA_ARGS__)
#define REPINF(...) DETAIL_OVERLOAD3(__VA_ARGS__, DETAIL_REPINF3, DETAIL_REPINF2, DETAIL_REPINF1)(__VA_ARGS__)

#define LOOP(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> DETAIL_UNIQVAR(loop_variable) = n; DETAIL_UNIQVAR(loop_variable) --> 0;)

#define ALL(iterable) std::begin(iterable), std::end(iterable)
#define INPUT(type, ...) type __VA_ARGS__; read(__VA_ARGS__)

// ! debug

#ifdef LOCAL
#  define debug(...) debug_internal(#__VA_ARGS__, __VA_ARGS__)

template <class T, class... Args>
void debug_internal(const char* s, T&& first, Args&&... args) {
    constexpr const char* prefix = "[\033[32mDEBUG\033[m] ";
    constexpr const char* open_brakets = sizeof...(args) == 0 ? "" : "(";
    constexpr const char* close_brakets = sizeof...(args) == 0 ? "" : ")";
    std::cerr << prefix << open_brakets << s << close_brakets << ": " << open_brakets << std::forward<T>(first);
    ((std::cerr << ", " << std::forward<Args>(args)), ...);
    std::cerr << close_brakets << "\n";
}

#else
#  define debug(...) void(0)
#endif

// ! I/O utilities

// __int128_t
std::ostream& operator<<(std::ostream& dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}
// __uint128_t
std::ostream& operator<<(std::ostream& dest, __uint128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[value % 10];
            value /= 10;
        } while (value != 0);
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}

// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U>& a) {
    return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...>& a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return out;
    else {
        out << std::get<N>(a);
        if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) out << ' ';
        return operator<<<N + 1>(out, a);
    }
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T>& a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N>& a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head& head, const Tail &...tails) {
    std::cout << head;
    if (sizeof...(tails)) std::cout << ' ';
    print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
    for (auto it = v.begin(); it != v.end();) {
        std::cout << *it;
        if (++it != v.end()) std::cout << sep;
    }
    std::cout << end;
}

__int128_t stoi128(const std::string& s) {
    __int128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    if (s[0] == '-') ret = -ret;
    return ret;
}
__uint128_t stou128(const std::string& s) {
    __uint128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    return ret;
}
// __int128_t
std::istream& operator>>(std::istream& in, __int128_t& v) {
    std::string s;
    in >> s;
    v = stoi128(s);
    return in;
}
// __uint128_t
std::istream& operator>>(std::istream& in, __uint128_t& v) {
    std::string s;
    in >> s;
    v = stou128(s);
    return in;
}
// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U>& a) {
    return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...>& a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return in;
    else return operator>><N + 1>(in >> std::get<N>(a), a);
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T>& a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N>& a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
template <typename ...Args>
void read(Args &...args) {
    (std::cin >> ... >> args);
}

// ! integral utilities

// Returns pow(-1, n)
template <typename T> constexpr inline int pow_m1(T n) {
    return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <> constexpr inline int pow_m1<bool>(bool n) {
    return -int(n) | 1;
}

// Returns floor(x / y)
template <typename T> constexpr inline T fld(const T x, const T y) {
    return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T> constexpr inline T cld(const T x, const T y) {
    return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}

template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(x); }
template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T> constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }
template <typename T> constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); }
template <typename T> constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T> constexpr inline int parity(const T x) { return popcount(x) & 1; }

// ! container

template <typename T, typename Comparator>
auto priqueue_comp(const Comparator comparator) {
    return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}

template <typename Container>
void sort_unique_erase(Container& a) {
    std::sort(a.begin(), a.end());
    a.erase(std::unique(a.begin(), a.end()), a.end());
}

template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
    if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container &&c, BiConsumer f) -> decltype(c.begin(), c.end(), void()) {
    foreach_adjacent_values(c.begin(), c.end(), f);
}

// ! other utilities

// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T& x, const T& y) {
    return y >= x ? false : (x = y, true);
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T& x, const T& y) {
    return y <= x ? false : (x = y, true);
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::string bin(T val, int bit_num = -1) {
    std::string res;
    if (bit_num != -1) {
        for (int bit = bit_num; bit-- > 0;) res += '0' + ((val >> bit) & 1);
    } else {
        for (; val; val >>= 1) res += '0' + (val & 1);
        std::reverse(res.begin(), res.end());
    }
    return res;
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_low_to_high(T val, T base = 10) {
    std::vector<T> res;
    for (; val; val /= base) res.push_back(val % base);
    if (res.empty()) res.push_back(T{ 0 });
    return res;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_high_to_low(T val, T base = 10) {
    auto res = digits_low_to_high(val, base);
    std::reverse(res.begin(), res.end());
    return res;
}

template <typename T>
std::string join(const std::vector<T>& v, const std::string& sep, const std::string& end) {
    std::ostringstream ss;
    for (auto it = v.begin(); it != v.end();) {
        ss << *it;
        if (++it != v.end()) ss << sep;
    }
    ss << end;
    return ss.str();
}

template <typename Func, typename Seq>
auto transform_to_vector(const Func &f, const Seq &s) {
    std::vector<std::invoke_result_t<Func, typename Seq::value_type>> v;
    v.reserve(std::size(s)), std::transform(std::begin(s), std::end(s), std::back_inserter(v), f);
    return v;
}
template <typename T, typename Seq>
auto copy_to_vector(const Seq &s) {
    std::vector<T> v;
    v.reserve(std::size(s)), std::copy(std::begin(s), std::end(s), std::back_inserter(v));
    return v;
}
template <typename Seq>
Seq concat(Seq s, const Seq &t) {
    s.reserve(std::size(s) + std::size(t));
    std::copy(std::begin(t), std::end(t), std::back_inserter(s));
    return s;
}
template <typename Seq>
std::vector<Seq> split(const Seq s, typename Seq::value_type delim) {
    std::vector<Seq> res;
    for (auto itl = std::begin(s), itr = itl;; itl = ++itr) {
        while (itr != std::end(s) and *itr != delim) ++itr;
        res.emplace_back(itl, itr);
        if (itr == std::end(s)) return res;
    }
}

int digit_to_int(char c) { return c - '0'; }
int lowercase_to_int(char c) { return c - 'a'; }
int uppercase_to_int(char c) { return c - 'A'; }

std::vector<int> digit_str_to_ints(const std::string &s) {
    return transform_to_vector(digit_to_int, s);
}
std::vector<int> lowercase_str_to_ints(const std::string &s) {
    return transform_to_vector(lowercase_to_int, s);
}
std::vector<int> uppercase_str_to_ints(const std::string &s) {
    return transform_to_vector(uppercase_to_int, s);
}

template <typename T, typename ToKey, typename CompareValue = std::less<>,
    std::enable_if_t<
        std::conjunction_v<
            std::is_invocable<ToKey, T>,
            std::is_invocable_r<bool, CompareValue, std::invoke_result_t<ToKey, T>, std::invoke_result_t<ToKey, T>
        >
    >, std::nullptr_t> = nullptr
>
auto comparator(const ToKey &to_key, const CompareValue &compare_value = std::less<>()) {
    return [to_key, compare_value](const T& x, const T& y) { return compare_value(to_key(x), to_key(y)); };
}

template <typename ToKey, std::enable_if_t<std::is_invocable_v<ToKey, int>, std::nullptr_t> = nullptr>
std::vector<int> sorted_indices(int n, const ToKey &to_key) {
    std::vector<int> p(n);
    std::iota(p.begin(), p.end(), 0);
    std::sort(p.begin(), p.end(), comparator<int>(to_key));
    return p;
}
template <typename Compare, std::enable_if_t<std::is_invocable_r_v<bool, Compare, int, int>, std::nullptr_t> = nullptr>
std::vector<int> sorted_indices(int n, const Compare &compare) {
    std::vector<int> p(n);
    std::iota(p.begin(), p.end(), 0);
    std::sort(p.begin(), p.end(), compare);
    return p;
}

const std::string Yes = "Yes", No = "No", YES = "YES", NO = "NO";

namespace suisen {}
using namespace suisen;
using namespace std;

struct io_setup {
    io_setup(int precision = 20) {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(precision);
    }
} io_setup_ {};

// ! code from here

#include <algorithm>
#include <cassert>
#include <complex>
#include <iostream>
#include <optional>
#include <tuple>
#include <variant>
#include <vector>

namespace suisen {
namespace geometry {

    using coordinate_t = long double;
    using Point = std::complex<coordinate_t>;

    // operator

    Point operator+(const Point &p, coordinate_t real) { return Point(p) + Point(real, 0); }
    Point operator-(const Point &p, coordinate_t real) { return Point(p) - Point(real, 0); }
    Point operator*(const Point &p, coordinate_t real) { return Point(p) * Point(real, 0); }
    Point operator/(const Point &p, coordinate_t real) { return Point(p) / Point(real, 0); }
    Point operator+(coordinate_t real, const Point &p) { return Point(real, 0) + Point(p); }
    Point operator-(coordinate_t real, const Point &p) { return Point(real, 0) - Point(p); }
    Point operator*(coordinate_t real, const Point &p) { return Point(real, 0) * Point(p); }
    Point operator/(coordinate_t real, const Point &p) { return Point(real, 0) / Point(p); }

    std::istream& operator>>(std::istream &in, Point &p) {
        coordinate_t x, y;
        in >> x >> y;
        p = Point(x, y);
        return in;
    }
    std::ostream& operator<<(std::ostream &out, const Point &p) {
        return out << p.real() << ' ' << p.imag();
    }

    // relations between three points X, Y, Z.

    struct ISP {
        static constexpr int L_CURVE = +1; // +---------------+ Z is in 'a' => ISP = +1
        static constexpr int R_CURVE = -1; // |aaaaaaaaaaaaaaa| Z is in 'b' => ISP = -1
        static constexpr int FRONT   = +2; // |ddd X eee Y ccc| Z is in 'c' => ISP = +2
        static constexpr int BACK    = -2; // |bbbbbbbbbbbbbbb| Z is in 'd' => ISP = -2
        static constexpr int MIDDLE  =  0; // +---------------+ Z is in 'e' => ISP =  0
    };

    struct Sign {
        static constexpr int NEGATIVE = -1;
        static constexpr int ZERO = 0;
        static constexpr int POSITIVE = +1;
    };

    enum class Containment {
        OUT, ON, IN
    };

    constexpr Point ZERO = Point(0, 0);
    constexpr Point ONE  = Point(1, 0);
    constexpr Point I    = Point(0, 1);
    constexpr coordinate_t EPS = 1e-9;
    constexpr coordinate_t PI  = 3.14159265358979323846264338327950288419716939937510L;
    constexpr coordinate_t E   = 2.71828182845904523536028747135266249775724709369995L;

    constexpr auto XY_COMPARATOR = [](const Point &p, const Point &q) {
        return p.real() == q.real() ? p.imag() < q.imag() : p.real() < q.real();
    };
    constexpr auto XY_COMPARATOR_GREATER = [](const Point &p, const Point &q) {
        return p.real() == q.real() ? p.imag() > q.imag() : p.real() > q.real();
    };
    constexpr auto YX_COMPARATOR = [](const Point &p, const Point &q) {
        return p.imag() == q.imag() ? p.real() < q.real() : p.imag() < q.imag();
    };
    constexpr auto YX_COMPARATOR_GREATER = [](const Point &p, const Point &q) {
        return p.imag() == q.imag() ? p.real() > q.real() : p.imag() > q.imag();
    };

    int sgn(coordinate_t x) {
        return x > EPS ? Sign::POSITIVE : x < -EPS ? Sign::NEGATIVE : Sign::ZERO;
    }
    int compare(coordinate_t x, coordinate_t y) {
        return sgn(x - y);
    }

    auto cartesian(const coordinate_t real, const coordinate_t imag) {
        return Point(real, imag);
    }
    auto polar(const coordinate_t rho, const coordinate_t theta) {
        return Point(rho * std::cos(theta), rho * std::sin(theta));
    }
    auto cis(const coordinate_t theta) {
        return Point(std::cos(theta), std::sin(theta));
    }
    auto conj(const Point &z) {
        return Point(z.real(), -z.imag());
    }
    auto arg(const Point &z) {
        return std::atan2(z.imag(), z.real());
    }
    auto square_abs(const Point &z) {
        return z.real() * z.real() + z.imag() * z.imag();
    }
    auto abs(const Point &z) {
        return std::sqrt(square_abs(z));
    }
    auto rot(const Point &z, const coordinate_t theta) {
        return cis(theta) * z;
    }
    auto dot(const Point &a, const Point &b) {
        return a.real() * b.real() + a.imag() * b.imag();
    }
    auto det(const Point &a, const Point &b) {
        return a.real() * b.imag() - a.imag() * b.real();
    }
    bool equals(const Point &a, const Point &b) {
        return sgn(a.real() - b.real()) == Sign::ZERO and sgn(a.imag() - b.imag()) == Sign::ZERO;
    }
    bool equals(coordinate_t a, coordinate_t b) {
        return compare(a, b) == 0;
    }
    
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C
    int isp(const Point &a, const Point &b, const Point &c) {
        Point ab = b - a, ac = c - a;
        int s = sgn(det(ab, ac));
        if (s == Sign::POSITIVE) return ISP::L_CURVE;
        if (s == Sign::NEGATIVE) return ISP::R_CURVE;
        if (sgn(dot(ab, ac)) == Sign::NEGATIVE) return ISP::BACK;
        Point ba = a - b, bc = c - b;
        if (sgn(dot(ba, bc)) == Sign::NEGATIVE) return ISP::FRONT;
        return ISP::MIDDLE;
    }

    struct Line {
        Point a, b;
        Line() : Line(ZERO, ZERO) {}
        Line(const Point &from, const Point &to) : a(from), b(to) {}
        // coef_x * x + coef_y * y + cnst = 0
        Line(coordinate_t coef_x, coordinate_t coef_y, coordinate_t cnst) {
            if (not equals(coef_x, 0.)) {
                a = { (coef_y - cnst) / coef_x, -1. };
                b = { (-coef_y - cnst) / coef_x, +1. };
            } else {
                a = { -1., (coef_x - cnst) / coef_y };
                b = { +1., (-coef_x - cnst) / coef_y };
            }
        }
    };
    struct Ray {
        Point a, b;
        Ray() : Ray(ZERO, ZERO) {}
        Ray(const Point &from, const Point &to) : a(from), b(to) {}
    };
    struct Segment {
        Point a, b;
        Segment() : Segment(ZERO, ZERO) {}
        Segment(const Point &from, const Point &to) : a(from), b(to) {}
    };
    struct Circle {
        Point center;
        coordinate_t radius;
        Circle() : Circle(ZERO, 0) {}
        Circle(const Point &c, const coordinate_t &r) : center(c), radius(r) {}
    };

    // Triangle
    
    coordinate_t signed_area(const Point &a, const Point &b, const Point &c) {
        return det(b - a, c - a) / 2;
    }
    coordinate_t area(const Point &a, const Point &b, const Point &c) {
        return std::abs(signed_area(a, b, c));
    }
    Point pG(const Point &a, const Point &b, const Point &c) {
        return (a + b + c) / 3;
    }
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_B
    Circle pI(const Point &a, const Point &b, const Point &c) {
        auto la = std::abs(b - c), lb = std::abs(c - a), lc = std::abs(a - b);
        auto l = la + lb + lc;
        la /= l, lb /= l, lc /= l;
        Point center = la * a + lb * b + lc * c;
        auto radius = 2. * area(a, b, c) / l;
        return Circle(center, radius);
    }
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_C
    Circle pO(const Point &a, const Point &b, const Point &c) {
        Point ab = b - a, bc = c - b, ca = a - c;
        auto la = square_abs(bc), lb = square_abs(ca), lc = square_abs(ab);
        auto s = la * (lb + lc - la), t = lb * (lc + la - lb), u = lc * (la + lb - lc);
        auto l = s + t + u;
        s /= l, t /= l, u /= l;
        Point center = a * s + b * t + c * u;
        return Circle(center, std::abs(center - a));
    }
    Point pH(const Point &a, const Point &b, const Point &c) {
        return a + b + c - 2 * pO(a, b, c).center;
    }
    auto pIabc(const Point &a, const Point &b, const Point &c) {
        return std::make_tuple(pI(-a, b, c), pI(a, -b, c), pI(a, b, -c));
    }

    // Line

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
    template <typename line_t_1, typename line_t_2>
    auto is_parallel(const line_t_1 &l1, const line_t_2 &l2) -> decltype(l1.a, l1.b, l2.a, l2.b, bool()) {
        return sgn(det(l1.b - l1.a, l2.b - l2.a)) == Sign::ZERO;
    }
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
    template <typename line_t_1, typename line_t_2>
    auto is_orthogonal(const line_t_1 &l1, const line_t_2 &l2) -> decltype(l1.a, l1.b, l2.a, l2.b, bool())  {
        return sgn(dot(l1.b - l1.a, l2.b - l2.a)) == Sign::ZERO;
    }
    template <typename line_t_1, typename line_t_2>
    auto on_the_same_line(const line_t_1 &l1, const line_t_2 &l2) -> decltype(l1.a, l1.b, l2.a, l2.b, bool())  {
        return is_parallel(l1, l2) and sgn(det(l1.b - l1.a, l2.a - l1.a)) == Sign::ZERO;
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A
    template <typename line_t>
    Point projection(const Point &p, const line_t &line) {
        Point a = p - line.a;
        Point b = line.b - line.a;
        return line.a + dot(a, b) / square_abs(b) * b;
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B
    template <typename line_t>
    Point reflection(const Point &p, const line_t &line) {
        Point h = projection(p, line);
        return p + (h - p) * 2;
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D
    coordinate_t square_distance(const Point &p, const Segment &l) {
        Point h = projection(p, l);
        if (isp(l.a, l.b, h) == ISP::MIDDLE) {
            return square_abs(h - p);
        } else {
            return std::min(square_abs(p - l.a), square_abs(p - l.b));
        }
    }
    coordinate_t square_distance(const Segment &l, const Point &p) {
        return square_distance(p, l);
    }
    coordinate_t square_distance(const Point &p, const Ray &l) {
        Point h = projection(p, l);
        int dir = isp(l.a, l.b, h);
        return dir == ISP::MIDDLE or dir == ISP::FRONT ? square_abs(h - p) : std::min(square_abs(p - l.a), square_abs(p - l.b));
    }
    coordinate_t square_distance(const Ray &l, const Point &p) {
        return square_distance(p, l);
    }
    coordinate_t square_distance(const Point &p, const Line &l) {
        return square_abs(projection(p, l) - p);
    }
    coordinate_t square_distance(const Line &l, const Point &p) {
        return square_distance(p, l);
    }
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D
    coordinate_t distance(const Point &p, const Segment &l) {
        return std::sqrt(square_distance(p, l));
    }
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D
    coordinate_t distance(const Segment &l, const Point &p) {
        return distance(p, l);
    }
    coordinate_t distance(const Point &p, const Ray &l) {
        return std::sqrt(square_distance(p, l));
    }
    coordinate_t distance(const Ray &l, const Point &p) {
        return distance(p, l);
    }
    coordinate_t distance(const Point &p, const Line &l) {
        return std::sqrt(square_distance(p, l));
    }
    coordinate_t distance(const Line &l, const Point &p) {
        return distance(p, l);
    }

    Containment contains(const Segment &l, const Point &p) {
        return sgn(distance(l, p)) == 0 ? Containment::ON : Containment::OUT;
    }
    Containment contains(const Ray &l, const Point &p) {
        return sgn(distance(l, p)) == 0 ? Containment::ON : Containment::OUT;
    }
    Containment contains(const Line &l, const Point &p) {
        return sgn(distance(l, p)) == 0 ? Containment::ON : Containment::OUT;
    }

    bool equals(const Line &l, const Line &m) {
        return on_the_same_line(l, m);
    }
    bool equals(const Ray &l, const Ray &m) {
        return on_the_same_line(l, m) and equals(l.a, m.a);
    }
    bool equals(const Segment &l, const Segment &m) {
        return (equals(l.a, m.a) and equals(l.b, m.b)) or (equals(l.a, m.b) and equals(l.b, m.a));
    }

    // "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B"
    bool has_common_point(const Segment &l1, const Segment &l2) {
        int isp_1a = isp(l1.a, l1.b, l2.a), isp_1b = isp(l1.a, l1.b, l2.b);
        if (isp_1a * isp_1b > 0) return false;
        int isp_2a = isp(l2.a, l2.b, l1.a), isp_2b = isp(l2.a, l2.b, l1.b);
        if (isp_2a * isp_2b > 0) return false;
        return true;
    }

    namespace internal {
        template <typename line_t_1, typename line_t_2>
        Point cross_point(const line_t_1 &l1, const line_t_2 &l2) {
            assert(not is_parallel(l1, l2));
            Point u = l1.b - l1.a, v = l2.a - l2.b, c = l2.a - l1.a;
            return l2.a - det(u, c) / det(u, v) * v;
        }
    }

    // "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_C"
    std::variant<std::nullptr_t, Point, Segment> common_point(const Segment &l1, const Segment &l2) {
        if (not has_common_point(l1, l2)) return nullptr;
        if (not is_parallel(l1, l2)) return internal::cross_point(l1, l2);
        std::vector<Point> ps { l1.a, l1.b, l2.a, l2.b };
        for (int i = 0; i <= 2; ++i) for (int j = 2; j >= i; --j) {
            if (XY_COMPARATOR(ps[j + 1], ps[j])) std::swap(ps[j], ps[j + 1]);
        }
        if (equals(ps[1], ps[2])) return ps[1];
        return Segment(ps[1], ps[2]);
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D
    coordinate_t square_distance(const Segment &l1, const Segment &l2) {
        if (has_common_point(l1, l2)) return 0;
        return std::min({ square_distance(l1, l2.a), square_distance(l1, l2.b), square_distance(l1.a, l2), square_distance(l1.b, l2) });
    }
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D
    coordinate_t distance(const Segment &l1, const Segment &l2) {
        return std::sqrt(square_distance(l1, l2));
    }

    // Polygon

    using Polygon = std::vector<Point>;

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A
    coordinate_t signed_area(const Polygon &poly) {
        coordinate_t res = 0;
        int sz = poly.size();
        for (int i = 0; i < sz; ++i) {
            int j = i + 1;
            if (j == sz) j = 0;
            res += signed_area(ZERO, poly[i], poly[j]);
        }
        return res;
    }
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A
    auto area(const Polygon &poly) {
        return std::abs(signed_area(poly));
    }
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B
    template <bool accept_180_degree = true>
    bool is_convex(const Polygon &poly) {
        int sz = poly.size();
        for (int i = 0; i < sz; ++i) {
            int j = i + 1, k = i + 2;
            if (j >= sz) j -= sz;
            if (k >= sz) k -= sz;
            int dir = isp(poly[i], poly[j], poly[k]);
            if constexpr (accept_180_degree) {
                if (dir == ISP::R_CURVE) return false;
            } else {
                if (dir != ISP::L_CURVE) return false;
            }
        }
        return true;
    }
    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C
    Containment contains(const Polygon &poly, const Point &p) {
        bool in = false;
        int sz = poly.size();
        for (int i = 0; i < sz; ++i) {
            int j = i + 1;
            if (j == sz) j -= sz;
            Point a = poly[i] - p, b = poly[j] - p;
            if (a.imag() > b.imag()) std::swap(a, b);
            if (sgn(a.imag()) <= 0 and sgn(b.imag()) > 0 and sgn(det(a, b)) < 0) in = not in;
            if (sgn(det(a, b)) == 0 and sgn(dot(a, b)) <= 0) return Containment::ON;
        }
        return in ? Containment::IN : Containment::OUT;
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_B
    std::tuple<int, int, coordinate_t> convex_diameter(const Polygon& convex) {
        const int sz = convex.size();
        if (sz <= 2) return { 0, sz - 1, abs(convex.front() - convex.back()) };
        auto [si, sj] = [&]{
            auto [it_min, it_max] = std::minmax_element(convex.begin(), convex.end(), XY_COMPARATOR);
            return std::pair<int, int> { it_min - convex.begin(), it_max - convex.begin() };
        }();
        coordinate_t max_dist = -1;
        std::pair<int, int> argmax{ -1, -1 };
        for (int i = si, j = sj; i != sj or j != si;) {
            if (coordinate_t dij = square_abs(convex[j] - convex[i]); dij > max_dist) max_dist = dij, argmax = { i, j };
            int ni = (i + 1) % sz, nj = (j + 1) % sz;
            if (det(convex[ni] - convex[i], convex[nj] - convex[j]) < 0) i = ni;
            else j = nj;
        }
        return { argmax.first, argmax.second, ::sqrtl(max_dist) };
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_C
    auto convex_cut(const Polygon &convex, const Line &l) {
        Polygon res;
        int sz = convex.size();
        for (int i = 0; i < sz; ++i) {
            int j = i + 1;
            if (j == sz) j -= sz;
            const Point &a = convex[i], &b = convex[j];
            int da = sgn(det(l.b - l.a, a - l.a));
            if (da >= 0) res.push_back(a);
            int db = sgn(det(l.b - l.a, b - l.a));
            if (da * db < 0) res.push_back(internal::cross_point(l, Segment(a, b)));
        }
        return res;
    }

    // Circle

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_A
    int tangent_num(const Circle &c1, const Circle &c2) {
        coordinate_t r1 = c1.radius, r2 = c2.radius;
        if (r1 > r2) return tangent_num(c2, c1);
        coordinate_t d = abs(c1.center - c2.center);
        int cp = compare(d, r1 + r2);
        if (cp > 0) return 4;
        if (cp == 0) return 3;
        int cn = compare(d, r2 - r1);
        if (cn > 0) return 2;
        if (cn == 0) return 1;
        return 0;
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D
    std::vector<Point> common_point(const Circle &c, const Line &l) {
        Point h = projection(c.center, l);
        coordinate_t d = abs(c.center - h);
        int cp = compare(d, c.radius);
        if (cp > 0) return {};
        if (cp == 0) return { h };
        auto v = (l.a - l.b) * (std::sqrt(c.radius * c.radius - d * d) / abs(l.a - l.b));
        return { h - v, h + v };
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H
    std::vector<Point> common_point(const Circle &c, const Segment &l) {
        auto ps = common_point(c, Line(l.a, l.b));
        ps.erase(std::remove_if(ps.begin(), ps.end(), [&](const auto &p) { return contains(l, p) != Containment::ON; }), ps.end());
        return ps;
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_E
    std::vector<Point> common_point(const Circle &c1, const Circle &c2) {
        coordinate_t r1 = c1.radius, r2 = c2.radius;
        if (r1 > r2) return common_point(c2, c1);
        coordinate_t d = abs(c1.center - c2.center);
        int cp = compare(d, r1 + r2), cn = compare(d, r2 - r1);
        if (cp > 0 or cn < 0) return {};
        auto v = c1.center - c2.center;
        coordinate_t lv = abs(v);
        if (cp == 0 or cn == 0) {
            return { c2.center + v * (r2 / lv) };
        }
        coordinate_t lp = d, ln = (r2 * r2 - r1 * r1) / d;
        coordinate_t p = (lp + ln) / 2, x = sqrt(r2 * r2 - p * p);
        auto h = c2.center + v * (p / lv);
        auto t = v * I;
        return { h + t * (x / lv), h - t * (x / lv) };
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_F
    Containment contains(const Circle &c, const Point &p) {
        coordinate_t d = abs(c.center - p);
        int cp = compare(d, c.radius);
        if (cp > 0) return Containment::OUT;
        if (cp < 0) return Containment::IN;
        return Containment::ON;
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_F
    std::vector<Point> tangent_to_circle(const Circle &c, const Point &p) {
        Containment cnt = contains(c, p);
        if (cnt == Containment::IN) return {};
        if (cnt == Containment::ON) return { p };
        auto v = c.center - p;
        coordinate_t r = c.radius, d = abs(v), l = sqrt(d * d - r * r);
        coordinate_t t = std::asin(r / d);
        return { p + rot(v, t) * (l / d), p + rot(v, -t) * (l / d) };
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_G
    // returns { Line(p, q) | p is on c1, q is on c2, Line(p, q) is common tangent of c1 and c2 }
    std::vector<Line> common_tangent(const Circle &c1, const Circle &c2) {
        int num = tangent_num(c1, c2);
        std::vector<Line> res;
        if (num == 0) return res;
        Point a = c1.center, b = c2.center, v = b - a;
        coordinate_t r1 = c1.radius, r2 = c2.radius;
        coordinate_t rp = r1 + r2, rm = r1 - r2, rd = r2 / r1;
        coordinate_t sqxy = square_abs(v);
        coordinate_t rtp = std::sqrt(std::max(sqxy - rp * rp, coordinate_t(0)));
        coordinate_t rtm = std::sqrt(std::max(sqxy - rm * rm, coordinate_t(0)));
        Point r = v * r1, u = r * Point(0, 1);
        Point l12 = r * rp, r12 = u * rtp, l34 = r * rm, r34 = u * rtm;
        Point p14 = (l34 + r34) / sqxy;
        res.emplace_back(a + p14, b + p14 * rd);
        if (num == 1) return res;
        Point p13 = (l34 - r34) / sqxy;
        res.emplace_back(a + p13, b + p13 * rd);
        if (num == 2) return res;
        Point p12 = (l12 + r12) / sqxy;
        res.emplace_back(a + p12, b - p12 * rd);
        if (num == 3) return res;
        Point p11 = (l12 - r12) / sqxy;
        res.emplace_back(a + p11, b - p11 * rd);
        return res;
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H
    coordinate_t intersection_area(const Polygon &poly, const Circle &circle) {
        int sz = poly.size();
        coordinate_t r2 = circle.radius * circle.radius;
        const Point &c = circle.center;
        coordinate_t area = 0;
        for (int i = 0; i < sz; i++) {
            int j = i + 1;
            if (j >= sz) j -= sz;
            Point a = poly[i], b = poly[j];
            bool in_a = contains(circle, a) == Containment::IN, in_b = contains(circle, b) == Containment::IN;
            Point ca = a - c, cb = b - c;
            if (in_a and in_b) {
                area += det(ca, cb);
                continue;
            }
            std::vector<Point> ps = common_point(circle, Segment(a, b));
            if (ps.empty()) {
                area += r2 * arg(cb / ca);
            } else {
                Point s = ps[0];
                Point t = ps.size() == 1 ? s : ps[1];
                if (compare(square_abs(t - a), square_abs(s - a)) < 0) std::swap(s, t);
                Point cs = s - c, ct = t - c;
                area += det(cs, ct);
                area += in_a ? det(ca, cs) : r2 * arg(cs / ca);
                area += in_b ? det(ct, cb) : r2 * arg(cb / ct);
            }
        }
        return area / 2;
    }

    // https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_I
    coordinate_t intersection_area(const Circle &c1, const Circle &c2) {
        coordinate_t r = c1.radius, s = c2.radius;
        if (r < s) return intersection_area(c2, c1);
        Point a = c1.center, b = c2.center;
        coordinate_t d = abs(a - b);
        if (compare(d, r + s) >= 0) return 0;
        if (compare(d, r - s) <= 0) return PI * s * s;
        coordinate_t x = (d * d + r * r - s * s) / (2 * d);
        coordinate_t h = std::sqrt(std::max(r * r - x * x, coordinate_t(0)));
        coordinate_t a1 = r * r * std::acos(x / r);
        coordinate_t a2 = s * s * std::acos((d - x) / s);
        coordinate_t a12 = d * h;
        return a1 + a2 - a12;
    }
}
} // namespace suisen

using namespace geometry;

constexpr coordinate_t inf = 1e100;

int main() {
    int n, m;
    read(n, m);

    vector<array<Point, 2>> points(n);
    for (auto &[p, q] : points) {
        coordinate_t x1, y1, x2, y2;
        read(x1, y1, x2, y2);
        p = { x1, y1 };
        q = { x2, y2 };
    }

    vector<array<int, 4>> st(n);

    REP(i, m) {
        int a, b, c, d;
        read(a, b, c, d);
        --a, --b, --c, --d;
        st[i] = { a, b, c, d };
    }

    vector<vector<coordinate_t>> g(2 * n, vector<coordinate_t>(2 * n, inf));
    REP(i, n) REP(ti, 2) {
        REP(j, n) REP(tj, 2) {
            Point x = points[i][ti];
            Point y = points[j][tj];
            Segment l1 { x, y };

            bool ok = true;
            REP(k, n) if (k != i and k != j) {
                Segment l2{ points[k][0], points[k][1] };
                if (has_common_point(l1, l2)) {
                    ok = false;
                    break;
                }
            }
            if (ok) {
                int fr = ti * n + i;
                int to = tj * n + j;
                coordinate_t dist = abs(x - y);
                g[fr][to] = dist;
            }
        }
    }
    REP(k, 2 * n) REP(i, 2 * n) REP(j, 2 * n) {
        chmin(g[i][j], g[i][k] + g[k][j]);
    }

    REP(qi, m) {
        auto [i, ti, j, tj] = st[qi];
        print(g[ti * n + i][tj * n + j]);
    }

    return 0;
}