#951258 (C++23) No.2628 Shrinkage

提出ソース
結果

問題	No.2628 Shrinkage
ユーザー	👑 seekworser
提出日時	2024-02-16 21:59:43
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	25,122 bytes
コンパイル時間	3,273 ms
コンパイル使用メモリ	254,292 KB
実行使用メモリ	6,548 KB
最終ジャッジ日時	2024-02-16 21:59:51
合計ジャッジ時間	4,276 ms
ジャッジサーバーID （参考情報）	judge14 / judge13
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,548 KB
testcase_01	AC	2 ms 6,548 KB
testcase_02	AC	2 ms 6,548 KB
testcase_03	AC	2 ms 6,548 KB
testcase_04	AC	2 ms 6,548 KB
testcase_05	AC	2 ms 6,548 KB
testcase_06	AC	2 ms 6,548 KB
testcase_07	AC	2 ms 6,548 KB
testcase_08	AC	2 ms 6,548 KB
testcase_09	AC	2 ms 6,548 KB
testcase_10	AC	2 ms 6,548 KB
testcase_11	AC	2 ms 6,548 KB
testcase_12	AC	2 ms 6,548 KB
testcase_13	AC	2 ms 6,548 KB
testcase_14	AC	2 ms 6,548 KB
testcase_15	AC	2 ms 6,548 KB
testcase_16	AC	2 ms 6,548 KB
testcase_17	AC	2 ms 6,548 KB
testcase_18	AC	2 ms 6,548 KB
testcase_19	AC	2 ms 6,548 KB
testcase_20	AC	2 ms 6,548 KB
testcase_21	AC	2 ms 6,548 KB
testcase_22	AC	2 ms 6,548 KB
testcase_23	AC	2 ms 6,548 KB
testcase_24	AC	2 ms 6,548 KB
testcase_25	AC	2 ms 6,548 KB
testcase_26	AC	2 ms 6,548 KB
testcase_27	AC	2 ms 6,548 KB
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ソースコード

raw source code
//line 1 "answer.cpp"
#if !__INCLUDE_LEVEL__
#include __FILE__
using P = Point<Frac>;
using L = Line<Frac>;
using L = Line<Frac>;
int solve() {
    P p1, p2, q1, q2;
    ll x,y;
    input(x, y); p1 = P(Frac(x, 1), Frac(y, 1));
    input(x, y); p2 = P(Frac(x, 1), Frac(y, 1));
    input(x, y); q1 = P(Frac(x, 1), Frac(y, 1));
    input(x, y); q2 = P(Frac(x, 1), Frac(y, 1));
    if (p1 == q1 && p2 == q2) return Yes();
    if ((p1 - p2).norm() <= (q1 - q2).norm()) return No();
    if (!is_parallel(p1 - p2, q1 - q2)) return No();
    if (dot((p1 - p2), (q1 - q2)) < 0) return No();
    Yes();
    return 0;
}
int main() {
    ll t; input(t);
    rep(t) solve();
}
#else
//line 2 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/std.hpp"
#include <bits/stdc++.h>
#ifndef LOCAL_TEST
#pragma GCC target ("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#endif // LOCAL_TEST
using namespace std;
// shorten typenames
using ll = long long;
using pii = pair<int, int>; using pll = pair<ll, ll>;
using vi = vector<int>;  using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>;  using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using vs = vector<string>; using vvs = vector<vector<string>>; using vvvs = vector<vector<vector<string>>>;
template<typename T> vector<vector<T>> vv(int h, int w, T val = T()) { return vector(h, vector<T>(w, val)); }
template<typename T> vector<vector<vector<T>>> vvv(int h1, int h2, int h3, T val = T()) { return vector(h1, vector(h2, vector<T>(h3, val))); }
template<typename T> vector<vector<vector<vector<T>>>> vvvv(int h1, int h2, int h3, int h4, T val = T()) { return vector(h1, vector(h2, vector(h3, vector<T>(h4, val)))); }
template <class T> using priority_queue_min = priority_queue<T, vector<T>, greater<T>>;
// define CONSTANTS
constexpr double PI = 3.14159265358979323;
constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL;
float EPS = 1e-8; double EPSL = 1e-10;
template<typename T> bool eq(const T x, const T y) { return x == y; }
template<> bool eq<double>(const double x, const double y) { return (abs(x - y) < EPSL * x || abs(x - y) < EPSL); }
template<> bool eq<float>(const float x, const float y) { return abs(x - y) < EPS * x; }
template<typename T> bool neq(const T x, const T y) { return !(eq<T>(x, y)); }
template<typename T> bool ge(const T x, const T y) { return (eq<T>(x, y) || (x > y)); }
template<typename T> bool le(const T x, const T y) { return (eq<T>(x, y) || (x < y)); }
template<typename T> bool gt(const T x, const T y) { return !(le<T>(x, y)); }
template<typename T> bool lt(const T x, const T y) { return !(ge<T>(x, y)); }
constexpr int MODINT998244353 = 998244353;
constexpr int MODINT1000000007 = 1000000007;
// fasten io
struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan;
// define macros
#define all(a) (a).begin(), (a).end()
#define sz(x) ((ll)(x).size())
#define rep1(n) for(ll dummy_iter = 0LL; dummy_iter < n; ++dummy_iter) // 0,1,...,n-1
#define rep2(i, n) for(ll i = 0LL, i##_counter = 0LL; i##_counter < ll(n); ++(i##_counter), (i) = i##_counter) // i=0,1,...,n-1
#define rep3(i, s, t) for(ll i = ll(s), i##_counter = ll(s); i##_counter < ll(t); ++(i##_counter), (i) = (i##_counter)) // i=s,s+1,...,t-1
#define rep4(i, s, t, step) for(ll i##_counter = step > 0 ? ll(s) : -ll(s), i##_end = step > 0 ? ll(t) : -ll(t), i##_step = abs(step), i = ll(s); i##_counter < i##_end; i##_counter += i##_step, i = step > 0 ? i##_counter : -i##_counter) // i=s,s+step,...,<t
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define repe(a, v) for(auto& a : (v)) // iterate over all elements in v
#define smod(n, m) ((((n) % (m)) + (m)) % (m))
#define sdiv(n, m) (((n) - smod(n, m)) / (m))
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());}
int Yes(bool b=true) { cout << (b ? "Yes\n" : "No\n"); return 0; };
int YES(bool b=true) { cout << (b ? "YES\n" : "NO\n"); return 0; };
int No(bool b=true) {return Yes(!b);};
int NO(bool b=true) {return YES(!b);};
template<typename T, size_t N> T max(array<T, N>& a) { return *max_element(all(a)); };
template<typename T, size_t N> T min(array<T, N>& a) { return *min_element(all(a)); };
template<typename T> T max(vector<T>& a) { return *max_element(all(a)); };
template<typename T> T min(vector<T>& a) { return *min_element(all(a)); };
template<typename T> vector<T> vec_slice(const vector<T>& a, int l, int r) { vector<T> rev; rep(i, l, r) rev.push_back(a[i]); return rev; };
template<typename T> T sum(vector<T>& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; };
template<typename T> bool in_range(const T& val, const T& s, const T& t) { return s <= val && val < t; };

template <class T> inline vector<T>& operator--(vector<T>& v) { repe(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repe(x, v) ++x; return v; }

ll powm(ll a, ll n, ll mod=INFL) {
    ll res = 1;
    while (n > 0) {
        if (n & 1) res = (res * a) % mod;
        if (n > 1) a = (a * a) % mod;
        n >>= 1;
    }
    return res;
}
ll sqrtll(ll x) {
    assert(x >= 0);
    ll rev = sqrt(x);
    while(rev * rev > x) --rev;
    while((rev+1) * (rev+1)<=x) ++rev;
    return rev;
}
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; }
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; }
int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; }
/**
 * @brief std.hpp
 * @docs docs/std/std.md
 */
//line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/geometry/base.hpp"
/**
 * @brief Pointクラス
 * @details
 * Point : 2次元空間上の点・ベクトルを扱うためのクラス
 * absもしくは単位ベクトルを使う場合はdoubleを使い、その他の場合はFracを使う
*/
template<typename T> struct Point {
    T x, y;
    Point(T x, T y) : x(x), y(y) {
    };
    Point() : Point(0, 0) {};

    Point<T> &operator+=(const Point<T>& p) { (*this).x += p.x; (*this).y += p.y; return *this; }
    Point<T> &operator-=(const Point<T>& p) { (*this).x -= p.x; (*this).y -= p.y; return *this; }
    friend Point<T> operator+(const Point<T>& lhs, const Point<T>& rhs) { return Point(lhs) += rhs; }
    friend Point<T> operator-(const Point<T>& lhs, const Point<T>& rhs) { return Point(lhs) -= rhs; }
    Point<T> &operator+() { return *this; }
    Point<T> &operator-() { (*this).x *= -1; (*this).y *= -1; return *this; }

    Point<T> &operator*=(const T &x) { (*this).x *= x; (*this).y *= x; return *this; }
    Point<T> &operator/=(const T &x) { (*this).x /= x; (*this).y /= x; return *this; }
    friend Point<T> operator*(const Point<T>& lhs, const T& rhs) { return Point(lhs) *= rhs; }
    friend Point<T> operator/(const Point<T>& lhs, const T& rhs) { return Point(lhs) /= rhs; }
    friend Point<T> operator*(const T& lhs, const Point<T>& rhs) { return Point(rhs) *= lhs; }
    friend Point<T> operator/(const T& lhs, const Point<T>& rhs) { return Point(rhs) /= lhs; }

    friend bool operator==(const Point<T> &lhs, const Point<T> &rhs) {
        return eq<T>(lhs.x, rhs.x) && eq<T>(lhs.y, rhs.y);
    }
    friend bool operator!=(const Point<T> &lhs, const Point<T> &rhs) {
        return !(lhs == rhs);
    }
    friend bool operator>(const Point<T>& lhs, const Point<T>& rhs) {
        if (eq<T>(lhs.x, rhs.x)) return gt<T>(lhs.y, rhs.y);
        return gt<T>(lhs.x, rhs.x);
    }
    friend bool operator<(const Point<T>& lhs, const Point<T>& rhs) {
        if (eq<T>(lhs.x, rhs.x)) return lt<T>(lhs.y, rhs.y);
        return lt<T>(lhs.x, rhs.x);
    }
    friend bool operator>=(const Point<T>& lhs, const Point<T>& rhs) { return !(lhs < rhs); }
    friend bool operator<=(const Point<T>& lhs, const Point<T>& rhs) { return !(lhs > rhs); }
    T dot(const Point<T> &p) const {return (*this).x * p.x + (*this).y * p.y; };
    T cross(const Point<T> &p) const {return (*this).x * p.y - (*this).y * p.x; };
    T norm() const {return (*this).dot(*this); };
    T abs() const {return sqrt((*this).norm()); };
    T arg() const {return atan((*this).y / (*this).x); };
    Point<T> rotate(const double &theta) {
        double nx = cos(theta) * (*this).x - sin(theta) * (*this).y;
        double ny = sin(theta) * (*this).x + cos(theta) * (*this).y;
        (*this).x = nx;
        (*this).y = ny;
        return (*this);
    };

    T operator*=(const Point<T>& p) const { return (*this).dot(p); }
    friend const T operator*(const Point<T>& lhs, const Point<T>& rhs) { return lhs *= rhs; }
    friend ostream& operator<<(ostream& os, const Point<T> &p) { os << p.x << " " << p.y; return os; }
};

template<typename T> T dot(const Point<T> &p1, const Point<T> &p2) { return p1.dot(p2); }
template<typename T> T cross(const Point<T> &p1, const Point<T> &p2) { return p1.cross(p2); }
template<typename T> T norm(const Point<T> &p) { return p.norm(); }
double abs(const Point<double> &p) { return p.abs(); }
Point<double> unit_vector(const Point<double> &p) { return p / abs(p); }
template<typename T> Point<T> normal_vector(const Point<double> &p) { return Point(-p.y, p.x); }
Point<double> rotate(const Point<double> &p, const double &theta) { return Point(p).rotate(theta); }

// Line : 直線クラス
template<typename T> struct Line {
    Point<T> s, t;
    Line() = default;
    Line(Point<T> s, Point<T> t) : s(s), t(t) {assert(s != t);};
    // ax+by+c=0;
    Line(T a, T b, T c) {
        assert(neq<T>(a, T(0)) || neq<T>(b, T(0)));
        if(eq<T>(b, T(0))) {
            s = Point(-c / a, T(0)); t = Point(-c / a, T(1));
        } else {
            s = Point(T(0), -c / b); t = Point(T(1), (-a-c)/b);
        }
    };
    Point<T> vec() const { return (*this).t - (*this).s; }
    Point<T> normal() const { return normal_vector((*this).vec()); }
    friend ostream& operator<<(ostream& os, const Line<T> &l) { os << l.s << " " << l.t; return os; }
};

// Segment : 線分を表す構造体
template <typename T> struct Segment : Line<T> {
    Segment() = default;
    Segment(Point<T> s, Point<T> t) : Line<T>(s, t) {}
};

// Circle : 円を表す構造体
// pが中心の位置ベクトル、rは半径
template<typename T> struct Circle {
    Point<T> o;
    T r;
    Circle() = default;
    Circle(Point<T> o, double r) : o(o), r(r) {}
};
/**
 * @brief 幾何ライブラリベースクラス
 * @docs docs/geometry/base.md
 */
//line 4 "/home/seekworser/.cpp_lib/competitive_library/competitive/geometry/counter_clockwise.hpp"
constexpr int COUNTER_CLOCKWISE = 2;
constexpr int CLOCKWISE = -2;
constexpr int ONSEGMENT = 0;
constexpr int ONLINE_BACK = 1;
constexpr int ONLINE_FRONT = -1;
template<typename T> int ccw(const Line<T> &l, const Point<T> &p, bool strict=false) {
    T crs = cross(l.vec(), p - l.s);
    if (lt<T>(crs, 0)) return CLOCKWISE;
    if (gt<T>(crs, 0)) return COUNTER_CLOCKWISE;
    T d = dot(l.vec(), p - l.s);
    if (strict) {
        if (le<T>(d, 0)) return ONLINE_BACK;
        if (ge<T>(d, norm(l.vec()))) return ONLINE_FRONT;
    } else {
        if (lt<T>(d, 0)) return ONLINE_BACK;
        if (gt<T>(d, norm(l.vec()))) return ONLINE_FRONT;
    }
    return ONSEGMENT;
};
template <typename T> int ccw(const Point<T> &p1, const Point<T> &p2, const Point<T> &p3, bool strict=false) {
    return ccw(Line<T>(p1, p2), p3, strict);
};
template <typename T> bool online(const Line<T> &l, const Point<T> &p) {
    int result = ccw(l, p);
    return -1 <= result && result <= 1;
};
template <typename T> int online(const Point<T> &p1, const Point<T> &p2, const Point<T> &p3) {
    return online(Line<T>(p1, p2), p3);
};
/**
 * @brief counter_clockwise.hpp
 * @docs docs/geometry/counter_clockwise.md
 */
//line 4 "/home/seekworser/.cpp_lib/competitive_library/competitive/geometry/angle.hpp"
constexpr int ANGLE_0 = 0;
constexpr int ANGLE_0_90 = 1;
constexpr int ANGLE_90 = 2;
constexpr int ANGLE_90_180 = 3;
constexpr int ANGLE_180 = 4;
constexpr int ANGLE_180_270 = -3;
constexpr int ANGLE_270 = -2;
constexpr int ANGLE_270_360 = -1;
template <typename T> int angle(const Point<T> &p1, const Point<T> &p2) {
    Point<T> zero(0, 0);
    assert(p1 != zero && p2 != zero);
    T d = dot(p1, p2);
    T c = cross(p1, p2);
    if (eq<T>(c, 0)) {
        if (gt<T>(d, 0)) return  ANGLE_0;
        else return ANGLE_180;
    }
    if (eq<T>(d, 0)) {
        if (gt<T>(c, 0)) return ANGLE_90;
        else return ANGLE_270;
    }
    if (gt<T>(d, 0) && gt<T>(c, 0)) return ANGLE_0_90;
    if (lt<T>(d, 0) && gt<T>(c, 0)) return ANGLE_90_180;
    if (lt<T>(d, 0) && lt<T>(c, 0)) return ANGLE_180_270;
    if (gt<T>(d, 0) && lt<T>(c, 0)) return ANGLE_270_360;
    throw runtime_error("function angle unexpectedly reached end");
};
template<typename T> int angle(const Line<T> &l1, const Line<T> &l2) { return angle(l1.vec(), l2.vec()); };
template<typename PointOrLine> bool is_parallel(const PointOrLine &p1, const PointOrLine &p2) {
    int result = angle(p1, p2);
    return result == ANGLE_0 || result == ANGLE_180;
}
template<typename PointOrLine> bool is_orthogonal(const PointOrLine &p1, const PointOrLine &p2) {
    int result = angle(p1, p2);
    return result == ANGLE_90 || result == ANGLE_270;
}
/**
 * @brief angle.hpp
 * @docs docs/geometry/angle.md
 */
//line 6 "/home/seekworser/.cpp_lib/competitive_library/competitive/geometry/intersection.hpp"
template <typename T> bool intersect(const Segment<T> &s1, const Segment<T> &s2, bool strict=false) {
    if (strict) {
        if (ccw(s1, s2.s, true) == ONSEGMENT) return online(s1, s2.t);
        if (ccw(s1, s2.t, true) == ONSEGMENT) return online(s1, s2.s);
        if (ccw(s2, s1.s, true) == ONSEGMENT) return online(s2, s1.t);
        if (ccw(s2, s1.t, true) == ONSEGMENT) return online(s2, s1.s);
        return
            ccw(s1, s2.s) * ccw(s1, s2.t) < 0 &&
            ccw(s2, s1.s) * ccw(s2, s1.t) < 0;
    }
    return
        ccw(s1, s2.s) * ccw(s1, s2.t) <= 0 &&
        ccw(s2, s1.s) * ccw(s2, s1.t) <= 0;
};
template<typename T> bool intersect(const Line<T> &l1, const Line<T> &l2) {
    if(!is_parallel(l1, l2)) return true;
    if (online(l1, l2.s)) return true;
    return false;
};
template<typename T> Point<T> cross_point(const Line<T> &l1, const Line<T> &l2) {
    assert(intersect(l1, l2));
    if(is_parallel(l1, l2)) return l1.s;
    T d1 = cross(l1.vec(), l2.vec());
    T d2 = cross(l1.vec(), l1.t - l2.s);
    return l2.s + l2.vec() * (d2 / d1);
};
template<typename T> Point<T> cross_point(const Segment<T> &s1, const Segment<T> &s2, bool strict=false) {
    assert(intersect(s1, s2, strict));
    if(is_parallel(s1, s2)) {
        if (ccw(s1, s2.s, strict) == ONSEGMENT) return s2.s;
        if (ccw(s1, s2.t, strict) == ONSEGMENT) return s2.t;
        if (ccw(s2, s1.s, strict) == ONSEGMENT) return s1.s;
        if (ccw(s2, s1.t, strict) == ONSEGMENT) return s1.t;
        throw("segments are parallel but cannot find cross point");
    }
    return cross_point(Line(s1), Line(s2));
};
/**
 * @brief intersection.hpp
 * @docs docs/geometry/intersection.md
 */
//line 6 "/home/seekworser/.cpp_lib/competitive_library/competitive/geometry/distance.hpp"
template <typename T> T norm(const Point<T> &p, const Line<T> &l) {
    T area_sq = cross(l.vec(), p - l.s);
    return area_sq * area_sq / norm(l.vec());
};
template<typename T> T norm(const Point<T> &p, const Segment<T> &s) {
    if (lt<T>(dot(s.vec(), p - s.s), 0)) return norm(p - s.s);
    if (lt<T>(dot(-s.vec(), p - s.t), 0)) return norm(p - s.t);
    return norm(p, Line<T>(s));
};
template <typename T> T norm(const Segment<T> &s1, const Segment<T> &s2) {
    if (intersect(s1, s2)) return T(0);
    T ans = norm(s1.s, s2);
    chmin(ans, norm(s1.t, s2));
    chmin(ans, norm(s2.s, s1));
    chmin(ans, norm(s2.t, s1));
    return ans;
};
double distance(const Point<double> &p, const Line<double> &l) { return sqrt(norm(p, l)); }
double distance(const Point<double> &p, const Segment<double> &s) { return sqrt(norm(p, s)); }
double distance(const Segment<double> &s1, const Segment<double> &s2) { return sqrt(norm(s1, s2)); }
template<typename T> T manhattan(const Point<T> &p) { return abs(p.x) + abs(p.y); }
template<typename T> T manhattan(const Point<T> &p1, const Point<T> &p2) { return manhattan(p1 - p2); }
/**
 * @brief distance.hpp
 * @docs docs/geometry/distance.md
 */
//line 29 "answer.cpp"
struct Frac {
    __int128_t num;
    __int128_t den;
    Frac (__int128_t _num, __int128_t _den, bool reduce = true) : num(_num), den(_den) {
        // if (reduce) (*this).reduce();
    }
    Frac (__int128_t _num) : Frac(_num, 1) {}
    static __int128_t redcue_limit;

    Frac inv() const { return Frac((*this).den, (*this).num); }
    Frac &operator+=(const Frac &x) {
        (*this).num = (*this).num * x.den + x.num * (*this).den;
        (*this).den = (*this).den * x.den;
        // if ((*this).den > redcue_limit || (*this).num > redcue_limit) (*this).reduce();
        return (*this);
    }
    Frac &operator-=(const Frac &x) {
        (*this).num = (*this).num * x.den - x.num * (*this).den;
        (*this).den = (*this).den * x.den;
        // if ((*this).den > redcue_limit || (*this).num > redcue_limit) (*this).reduce();
        return (*this);
    }
    Frac &operator*=(const Frac &x) {
        (*this).num = (*this).num * x.num;
        (*this).den = (*this).den * x.den;
        // if ((*this).den > redcue_limit || (*this).num > redcue_limit) (*this).reduce();
        return (*this);
    }
    Frac &operator/=(const Frac &x) {
        (*this) *= x.inv();
        // if ((*this).den > redcue_limit || (*this).num > redcue_limit) (*this).reduce();
        return (*this);
    }
    Frac operator+(const Frac &x) const { return (Frac(*this) += x); }
    Frac operator-(const Frac &x) const { return (Frac(*this) -= x); }
    Frac operator*(const Frac &x) const { return (Frac(*this) *= x); }
    Frac operator/(const Frac &x) const { return (Frac(*this) /= x); }

    Frac operator+() const { return *this; }
    Frac operator-() const { Frac x(-(*this).num, (*this).den); return x; }
    friend bool operator==(const Frac& lhs, const Frac& rhs) {
        return lhs.num * rhs.den == lhs.den * rhs.num;
    }
    friend bool operator!=(const Frac& lhs, const Frac& rhs) {
        return lhs.num * rhs.den != lhs.den * rhs.num;
    }
    friend bool operator>=(const Frac& lhs, const Frac& rhs) {
        return lhs.num * rhs.den >= lhs.den * rhs.num;
    }
    friend bool operator<=(const Frac& lhs, const Frac& rhs) {
        return lhs.num * rhs.den <= lhs.den * rhs.num;
    }
    friend bool operator>(const Frac& lhs, const Frac& rhs) {
        return lhs.num * rhs.den > lhs.den * rhs.num;
    }
    friend bool operator<(const Frac& lhs, const Frac& rhs) {
        return lhs.num * rhs.den < lhs.den * rhs.num;
    }

    double val() const {return (double)((*this).num) / (double)((*this).den); }
    friend ostream& operator<<(ostream& os, const Frac &x) { os << x.val(); return os; }
    // void reduce() {
    //     assert((*this).den != 0 || (*this).num != 0);
    //     if ((*this).den == 0) { (*this).num = 1; return; }
    //     if ((*this).num == 0) { (*this).den = 1; return; }
    //     __int128_t g = gcd((*this).num, (*this).den);
    //     (*this).num /= g;
    //     (*this).den /= g;
    //     if ((*this).den < 0) {
    //         (*this).num *= -1;
    //         (*this).den *= -1;
    //     }
    //     return;
    // }
};
__int128_t Frac::redcue_limit = 1000000000;
Frac abs(const Frac &f) {
    Frac rev(f);
    if (rev.den * rev.num < 0) return -rev;
    return rev;
}
//line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/io.hpp"
// overload operators (prototypes)
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p);
template <class T> inline istream& operator>>(istream& is, vector<T>& v);
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v);
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp);
template <typename T> ostream &operator<<(ostream &os, const set<T> &st);
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st);
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st);
template <typename T> ostream &operator<<(ostream &os, queue<T> q);
template <typename T> ostream &operator<<(ostream &os, deque<T> q);
template <typename T> ostream &operator<<(ostream &os, stack<T> st);
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq);

// overload operators
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repe(x, v) is >> x; return is; }
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p) { os << p.first << " " << p.second; return os; }
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st) { ll cnt = 0; for (auto &e : st) { os << e << (++cnt != (int)st.size() ? " " : ""); } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q) { while (q.size()) { os << q.front(); q.pop_front(); if (q.size()) os << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; }

template <typename T> int print_sep_end(string sep, string end, const T& val) { (void)sep; cout << val << end; return 0; };
template <typename T1, typename... T2> int print_sep_end(string sep, string end, const T1 &val, const T2 &...remain) {
    cout << val << sep;
    print_sep_end(sep, end, remain...);
    return 0;
};
template <typename... T> int print(const T &...args) { print_sep_end(" ", "\n", args...); return 0; };
template <typename... T> void flush() { cout << flush; };
template <typename... T> int print_and_flush(const T &...args) { print(args...); flush(); return 0; };
#define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug print
template <typename T> void input(T &a) { cin >> a; };
template <typename T1, typename... T2> void input(T1&a, T2 &...b) { cin >> a; input(b...); };
#ifdef LOCAL_TEST
template <typename T> void debug_func(int i, const T name) { (void)i; (void)name; cerr << endl; }
template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) {
    int scope = 0;
    for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {
        cerr << name[i];
        if (name[i] == '(' || name[i] == '{') scope++;
        if (name[i] == ')' || name[i] == '}') scope--;
    }
    cerr << ":" << a << " ";
    debug_func(i + 1, name, b...);
}
template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, T2 &a, T3 &...b) {
    int scope = 0;
    for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {
        cerr << name[i];
        if (name[i] == '(' || name[i] == '{') scope++;
        if (name[i] == ')' || name[i] == '}') scope--;
    }
    cerr << ":" << a << " ";
    debug_func(i + 1, name, b...);
}
#endif
#ifndef LOCAL_TEST
template <typename... T>
void debug_func(T &...) {}
template <typename... T>
void debug_func(const T &...) {}
#endif
/**
 * @brief io.hpp
 * @docs docs/std/io.md
 */
//line 111 "answer.cpp"
#endif
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