#574496 (C++17) No.199 星を描こう

• 問題: No.199 星を描こう
• ユーザー: yuruhiya
• 提出日時: 2020-11-02 16:59:11
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 48,222 bytes
• コンパイル時間: 3,280 ms
• コンパイル使用メモリ: 223,416 KB
• 最終ジャッジ日時: 2025-01-15 19:04:49
• ジャッジサーバーID （参考情報）: judge1 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 25

ソースコード

#line 2 "/home/yuruhiya/programming/library/template/template.cpp"
#include <bits/stdc++.h>
#line 6 "/home/yuruhiya/programming/library/template/constants.cpp"
using namespace std;

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define rrep(i, n) for (int i = (n)-1; i >= 0; --i)
#define rfor(i, m, n) for (int i = (m); i >= (n); --i)
#define unless(c) if (!(c))
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define range_it(a, l, r) (a).begin() + (l), (a).begin() + (r)

using namespace std;
using ll = long long;
using LD = long double;
using VB = vector<bool>;
using VVB = vector<VB>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using VS = vector<string>;
using VD = vector<LD>;
using PII = pair<int, int>;
using VP = vector<PII>;
using PLL = pair<ll, ll>;
using VPL = vector<PLL>;
template <class T> using PQ = priority_queue<T>;
template <class T> using PQS = priority_queue<T, vector<T>, greater<T>>;
constexpr int inf = 1e9;
constexpr long long inf_ll = 1e18, MOD = 1000000007;
constexpr long double PI = 3.14159265358979323846, EPS = 1e-12;
#line 7 "/home/yuruhiya/programming/library/template/Input.cpp"
using namespace std;

#ifdef _WIN32
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#define fwrite_unlocked fwrite
#define fflush_unlocked fflush
#endif
class Input {
	static int gc() {
		return getchar_unlocked();
	}
	template <class T> static void i(T& v) {
		cin >> v;
	}
	static void i(char& v) {
		while (isspace(v = gc()))
			;
	}
	static void i(bool& v) {
		v = in<char>() != '0';
	}
	static void i(string& v) {
		v.clear();
		char c;
		for (i(c); !isspace(c); c = gc())
			v += c;
	}
	static void i(int& v) {
		bool neg = false;
		v = 0;
		char c;
		i(c);
		if (c == '-') {
			neg = true;
			c = gc();
		}
		for (; isdigit(c); c = gc())
			v = v * 10 + (c - '0');
		if (neg) v = -v;
	}
	static void i(long long& v) {
		bool neg = false;
		v = 0;
		char c;
		i(c);
		if (c == '-') {
			neg = true;
			c = gc();
		}
		for (; isdigit(c); c = gc())
			v = v * 10 + (c - '0');
		if (neg) v = -v;
	}
	static void i(double& v) {
		double dp = 1;
		bool neg = false, adp = false;
		v = 0;
		char c;
		i(c);
		if (c == '-') {
			neg = true;
			c = gc();
		}
		for (; isdigit(c) || c == '.'; c = gc()) {
			if (c == '.')
				adp = true;
			else if (adp)
				v += (c - '0') * (dp *= 0.1);
			else
				v = v * 10 + (c - '0');
		}
		if (neg) v = -v;
	}
	static void i(long double& v) {
		long double dp = 1;
		bool neg = false, adp = false;
		v = 0;
		char c;
		i(c);
		if (c == '-') {
			neg = true;
			c = gc();
		}
		for (; isdigit(c) || c == '.'; c = gc()) {
			if (c == '.')
				adp = true;
			else if (adp)
				v += (c - '0') * (dp *= 0.1);
			else
				v = v * 10 + (c - '0');
		}
		if (neg) v = -v;
	}
	template <class T, class U> static void i(pair<T, U>& v) {
		i(v.first);
		i(v.second);
	}
	template <class T> static void i(vector<T>& v) {
		for (auto& e : v)
			i(e);
	}
	template <size_t N = 0, class T> static void input_tuple(T& v) {
		if constexpr (N < tuple_size_v<T>) {
			i(get<N>(v));
			input_tuple<N + 1>(v);
		}
	}
	template <class... T> static void i(tuple<T...>& v) {
		input_tuple(v);
	}
	struct InputV {
		int n, m;
		InputV(int _n) : n(_n), m(0) {}
		InputV(const pair<int, int>& nm) : n(nm.first), m(nm.second) {}
		template <class T> operator vector<T>() {
			vector<T> v(n);
			i(v);
			return v;
		}
		template <class T> operator vector<vector<T>>() {
			vector<vector<T>> v(n, vector<T>(m));
			i(v);
			return v;
		}
	};

public:
	static string read_line() {
		string v;
		char c;
		for (i(c); c != '\n' && c != '\0'; c = gc())
			v += c;
		return v;
	}
	template <class T> static T in() {
		T v;
		i(v);
		return v;
	}
	template <class T> operator T() const {
		return in<T>();
	}
	int operator--(int) const {
		return in<int>() - 1;
	}
	InputV operator[](int n) const {
		return InputV(n);
	}
	InputV operator[](const pair<int, int>& n) const {
		return InputV(n);
	}
	void operator()() const {}
	template <class H, class... T> void operator()(H&& h, T&&... t) const {
		i(h);
		operator()(forward<T>(t)...);
	}

private:
	template <template <class...> class, class...> struct Multiple;
	template <template <class...> class V, class Head, class... Tail> struct Multiple<V, Head, Tail...> {
		template <class... Args> using vec = V<vector<Head>, Args...>;
		using type = typename Multiple<vec, Tail...>::type;
	};
	template <template <class...> class V> struct Multiple<V> { using type = V<>; };
	template <class... T> using multiple_t = typename Multiple<tuple, T...>::type;
	template <size_t N = 0, class T> void in_multiple(T& t) const {
		if constexpr (N < tuple_size_v<T>) {
			auto& vec = get<N>(t);
			using V = typename remove_reference_t<decltype(vec)>::value_type;
			vec.push_back(in<V>());
			in_multiple<N + 1>(t);
		}
	}

public:
	template <class... T> auto multiple(int H) const {
		multiple_t<T...> res;
		while (H--)
			in_multiple(res);
		return res;
	}
} in;
#define input(T) Input::in<T>()
#define INT input(int)
#define LL input(long long)
#define STR input(string)
#define inputs(T, ...) \
	T __VA_ARGS__;     \
	in(__VA_ARGS__)
#define ini(...) inputs(int, __VA_ARGS__)
#define inl(...) inputs(long long, __VA_ARGS__)
#define ins(...) inputs(string, __VA_ARGS__)
#line 6 "/home/yuruhiya/programming/library/template/Output.cpp"
#include <charconv>
#line 9 "/home/yuruhiya/programming/library/template/Output.cpp"
using namespace std;

struct BoolStr {
	const char *t, *f;
	BoolStr(const char* _t, const char* _f) : t(_t), f(_f) {}
} Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0");
struct DivStr {
	const char *d, *l;
	DivStr(const char* _d, const char* _l) : d(_d), l(_l) {}
} spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"), no_endl(" ", "");
class Output {
	BoolStr B{Yes};
	DivStr D{spc};
	void p(int v) const {
		char buf[12]{};
		if (auto [ptr, e] = to_chars(begin(buf), end(buf), v); e == errc{}) {
			fwrite(buf, sizeof(char), ptr - buf, stdout);
		} else {
			assert(false);
		}
	}
	void p(long long v) const {
		char buf[21]{};
		if (auto [ptr, e] = to_chars(begin(buf), end(buf), v); e == errc{}) {
			fwrite(buf, sizeof(char), ptr - buf, stdout);
		} else {
			assert(false);
		}
	}
	void p(bool v) const {
		p(v ? B.t : B.f);
	}
	void p(char v) const {
		putchar_unlocked(v);
	}
	void p(const char* v) const {
		fwrite_unlocked(v, 1, strlen(v), stdout);
	}
	void p(double v) const {
		printf("%.20f", v);
	}
	void p(long double v) const {
		printf("%.20Lf", v);
	}
	template <class T> void p(const T& v) const {
		cout << v;
	}
	template <class T, class U> void p(const pair<T, U>& v) const {
		p(v.first);
		p(D.d);
		p(v.second);
	}
	template <class T> void p(const vector<T>& v) const {
		rep(i, sz(v)) {
			if (i) p(D.d);
			p(v[i]);
		}
	}
	template <class T> void p(const vector<vector<T>>& v) const {
		rep(i, sz(v)) {
			if (i) p(D.l);
			p(v[i]);
		}
	}

public:
	Output& operator()() {
		p(D.l);
		return *this;
	}
	template <class H> Output& operator()(H&& h) {
		p(h);
		p(D.l);
		return *this;
	}
	template <class H, class... T> Output& operator()(H&& h, T&&... t) {
		p(h);
		p(D.d);
		return operator()(forward<T>(t)...);
	}
	template <class It> Output& range(const It& l, const It& r) {
		for (It i = l; i != r; i++) {
			if (i != l) p(D.d);
			p(*i);
		}
		p(D.l);
		return *this;
	}
	template <class T> Output& range(const T& a) {
		range(a.begin(), a.end());
		return *this;
	}
	template <class... T> void exit(T&&... t) {
		operator()(forward<T>(t)...);
		std::exit(EXIT_SUCCESS);
	}
	Output& flush() {
		fflush_unlocked(stdout);
		return *this;
	}
	Output& set(const BoolStr& b) {
		B = b;
		return *this;
	}
	Output& set(const DivStr& d) {
		D = d;
		return *this;
	}
	Output& set(const char* t, const char* f) {
		B = BoolStr(t, f);
		return *this;
	}
} out;
#line 3 "/home/yuruhiya/programming/library/template/Step.cpp"
using namespace std;

template <class T> struct Step {
	class It {
		T a, b, c;

	public:
		constexpr It() : a(T()), b(T()), c(T()) {}
		constexpr It(T _b, T _c, T _s) : a(_b), b(_c), c(_s) {}
		constexpr It& operator++() {
			--b;
			a += c;
			return *this;
		}
		constexpr It operator++(int) {
			It tmp = *this;
			--b;
			a += c;
			return tmp;
		}
		constexpr const T& operator*() const {
			return a;
		}
		constexpr const T* operator->() const {
			return &a;
		}
		constexpr bool operator==(const It& i) const {
			return b == i.b;
		}
		constexpr bool operator!=(const It& i) const {
			return !(b == i.b);
		}
		constexpr T start() const {
			return a;
		}
		constexpr T size() const {
			return b;
		}
		constexpr T step() const {
			return c;
		}
	};
	constexpr Step(T b, T c, T s) : be(b, c, s) {}
	constexpr It begin() const {
		return be;
	}
	constexpr It end() const {
		return en;
	}
	constexpr T start() const {
		return be.start();
	}
	constexpr T size() const {
		return be.size();
	}
	constexpr T step() const {
		return be.step();
	}
	constexpr T sum() const {
		return start() * size() + step() * (size() * (size() - 1) / 2);
	}
	operator vector<T>() const {
		return to_a();
	}
	auto to_a() const {
		vector<T> res;
		res.reserve(size());
		for (auto i : *this) {
			res.push_back(i);
		}
		return res;
	}
	using value_type = T;
	using iterator = It;

private:
	It be, en;
};
template <class T> inline constexpr auto step(T a) {
	return Step<T>(0, a, 1);
}
template <class T> inline constexpr auto step(T a, T b) {
	return Step<T>(a, b - a, 1);
}
template <class T> inline constexpr auto step(T a, T b, T c) {
	return Step<T>(a, a < b ? (b - a - 1) / c + 1 : 0, c);
}
#line 8 "/home/yuruhiya/programming/library/template/Ruby.cpp"
using namespace std;

template <class F> struct Callable {
	F func;
	Callable(const F& f) : func(f) {}
};
template <class T, class F> auto operator|(const T& v, const Callable<F>& c) {
	return c.func(v);
}

struct Sort_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			sort(begin(v), end(v), f);
			return v;
		});
	}
	template <class T> friend auto operator|(T v, [[maybe_unused]] const Sort_impl& c) {
		sort(begin(v), end(v));
		return v;
	}
} Sort;
struct SortBy_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			sort(begin(v), end(v), [&](const auto& i, const auto& j) {
				return f(i) < f(j);
			});
			return v;
		});
	}
} SortBy;
struct RSort_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			sort(rbegin(v), rend(v), f);
			return v;
		});
	}
	template <class T> friend auto operator|(T v, [[maybe_unused]] const RSort_impl& c) {
		sort(rbegin(v), rend(v));
		return v;
	}
} RSort;
struct RSortBy_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			sort(begin(v), end(v), [&](const auto& i, const auto& j) {
				return f(i) > f(j);
			});
			return v;
		});
	}
} RSortBy;
struct Reverse_impl {
	template <class T> friend auto operator|(T v, const Reverse_impl& c) {
		reverse(begin(v), end(v));
		return v;
	}
} Reverse;
struct Unique_impl {
	template <class T> friend auto operator|(T v, const Unique_impl& c) {
		v.erase(unique(begin(v), end(v), end(v)));
		return v;
	}
} Unique;
struct Uniq_impl {
	template <class T> friend auto operator|(T v, const Uniq_impl& c) {
		sort(begin(v), end(v));
		v.erase(unique(begin(v), end(v)), end(v));
		return v;
	}
} Uniq;
struct Rotate_impl {
	auto operator()(int&& left) {
		return Callable([&](auto v) {
			int s = static_cast<int>(size(v));
			assert(-s <= left && left <= s);
			if (0 <= left) {
				rotate(begin(v), begin(v) + left, end(v));
			} else {
				rotate(begin(v), end(v) + left, end(v));
			}
			return v;
		});
	}
} Rotate;
struct Max_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			return *max_element(begin(v), end(v), f);
		});
	}
	template <class T> friend auto operator|(T v, const Max_impl& c) {
		return *max_element(begin(v), end(v));
	}
} Max;
struct Min_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			return *min_element(begin(v), end(v), f);
		});
	}
	template <class T> friend auto operator|(T v, const Min_impl& c) {
		return *min_element(begin(v), end(v));
	}
} Min;
struct MaxPos_impl {
	template <class T> friend auto operator|(T v, const MaxPos_impl& c) {
		return max_element(begin(v), end(v)) - begin(v);
	}
} MaxPos;
struct MinPos_impl {
	template <class T> friend auto operator|(T v, const MinPos_impl& c) {
		return min_element(begin(v), end(v)) - begin(v);
	}
} MinPos;
struct MaxBy_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			auto max_it = begin(v);
			auto max_val = f(*max_it);
			for (auto it = next(begin(v)); it != end(v); ++it) {
				if (auto val = f(*it); max_val < val) {
					max_it = it;
					max_val = val;
				}
			}
			return *max_it;
		});
	}
} MaxBy;
struct MinBy_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			auto min_it = begin(v);
			auto min_val = f(*min_it);
			for (auto it = next(begin(v)); it != end(v); ++it) {
				if (auto val = f(*it); min_val > val) {
					min_it = it;
					min_val = val;
				}
			}
			return *min_it;
		});
	}
} MinBy;
struct MaxOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			auto max_val = f(*begin(v));
			for (auto it = next(begin(v)); it != end(v); ++it) {
				if (auto val = f(*it); max_val < val) {
					max_val = val;
				}
			}
			return max_val;
		});
	}
} MaxOf;
struct MinOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			auto min_val = f(*begin(v));
			for (auto it = next(begin(v)); it != end(v); ++it) {
				if (auto val = f(*it); min_val > val) {
					min_val = val;
				}
			}
			return min_val;
		});
	}
} MinOf;
struct Count_impl {
	template <class V> auto operator()(const V& val) {
		return Callable([&](auto v) {
			return count(begin(v), end(v), val);
		});
	}
} Count;
struct CountIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) {
			return count_if(begin(v), end(v), f);
		});
	}
} CountIf;
struct Index_impl {
	template <class V> auto operator()(const V& val) {
		return Callable([&](auto v) -> optional<int> {
			auto res = find(begin(v), end(v), val);
			return res != end(v) ? optional(res - begin(v)) : nullopt;
		});
	}
} Index;
struct IndexIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) -> optional<int> {
			auto res = find_if(begin(v), end(v), f);
			return res != end(v) ? optional(res - begin(v)) : nullopt;
		});
	}
} IndexIf;
struct FindIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) -> optional<typename decltype(v)::value_type> {
			auto res = find_if(begin(v), end(v), f);
			return res != end(v) ? optional(*res) : nullopt;
		});
	}
} FindIf;
struct Sum_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			return accumulate(next(begin(v)), end(v), f(*begin(v)), [&](const auto& a, const auto& b) {
				return a + f(b);
			});
		});
	}
	template <class T> friend auto operator|(T v, const Sum_impl& c) {
		return accumulate(begin(v), end(v), typename T::value_type{});
	}
} Sum;
struct Includes {
	template <class V> auto operator()(const V& val) {
		return Callable([&](auto v) {
			return find(begin(v), end(v), val) != end(v);
		});
	}
} Includes;
struct IncludesIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) {
			return find_if(begin(v), end(v), f) != end(v);
		});
	}
} IncludesIf;
struct RemoveIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) {
			v.erase(remove_if(begin(v), end(v), f), end(v));
			return v;
		});
	}
} RemoveIf;
struct Each_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			for (const auto& i : v) {
				f(i);
			}
		});
	}
} Each;
struct Select_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			using value_type = typename decltype(v)::value_type;
			vector<value_type> res;
			for (const auto& i : v) {
				if (f(i)) res.push_back(i);
			}
			return res;
		});
	}
} Select;
struct Map_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			using result_type = invoke_result_t<F, typename decltype(v)::value_type>;
			vector<result_type> res;
			res.reserve(size(v));
			for (const auto& i : v) {
				res.push_back(f(i));
			}
			return res;
		});
	}
} Map;
struct Indexed_impl {
	template <class T> friend auto operator|(const T& v, Indexed_impl& c) {
		using value_type = typename T::value_type;
		vector<pair<value_type, int>> res;
		res.reserve(size(v));
		int index = 0;
		for (const auto& i : v) {
			res.emplace_back(i, index++);
		}
		return res;
	}
} Indexed;
struct AllOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			for (const auto& i : v) {
				if (!f(i)) return false;
			}
			return true;
		});
	}
} AllOf;
struct AnyOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			for (const auto& i : v) {
				if (f(i)) return true;
			}
			return false;
		});
	}
} AnyOf;
struct NoneOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			for (const auto& i : v) {
				if (f(i)) return false;
			}
			return true;
		});
	}
} NoneOf;

struct Tally_impl {
	template <class F> auto operator()(size_t max_val) {
		return Callable([&](auto v) {
			vector<size_t> res(max_val);
			for (const auto& i : v) {
				res[static_cast<size_t>(i)]++;
			}
			return res;
		});
	}
	template <class T, class value_type = typename T::value_type> friend auto operator|(const T& v, Tally_impl& c) {
		map<value_type, size_t> res;
		for (const auto& i : v) {
			res[i]++;
		}
		return res;
	}
} Tally;

template <class T> auto operator*(const vector<T>& a, size_t n) {
	T res;
	for (size_t i = 0; i < n; ++i) {
		res.insert(res.end(), a.begin(), a.end());
	}
	return res;
}
auto operator*(string a, size_t n) {
	string res;
	for (size_t i = 0; i < n; ++i) {
		res += a;
	}
	return res;
}
template <class T, class U> auto& operator<<(vector<T>& a, const U& b) {
	a.insert(a.end(), all(b));
	return a;
}
template <class T> auto& operator<<(string& a, const T& b) {
	a.insert(a.end(), all(b));
	return a;
}
template <class T, class U> auto operator+(vector<T> a, const U& b) {
	a << b;
	return a;
}
template <class T> auto operator+(string a, const T& b) {
	a << b;
	return a;
}
#line 6 "/home/yuruhiya/programming/library/template/functions.cpp"
using namespace std;

template <class T, class U> inline int Lower(const T& a, const U& v) {
	return lower_bound(all(a), v) - a.begin();
}
template <class T, class U> inline int Upper(const T& a, const U& v) {
	return upper_bound(all(a), v) - a.begin();
}
template <class T> inline auto Slice(const T& v, size_t i, size_t len) {
	return i < v.size() ? T(v.begin() + i, v.begin() + min(i + len, v.size())) : T();
}
template <class T> inline T Ceil(T n, T m) {
	return (n + m - 1) / m;
}
template <class T> inline T Ceil2(T n, T m) {
	return Ceil(n, m) * m;
}
template <class T> inline T Tri(T n) {
	return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1);
}
template <class T> inline T nC2(T n) {
	return (n & 1) ? (n - 1) / 2 * n : n / 2 * (n - 1);
}
template <class T> inline T Mid(const T& l, const T& r) {
	return l + (r - l) / 2;
}
template <class T> inline bool chmax(T& a, const T& b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}
template <class T> inline bool chmin(T& a, const T& b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}
template <class T> inline bool inRange(const T& v, const T& min, const T& max) {
	return min <= v && v < max;
}
template <class T> inline bool isSquere(T n) {
	T s = sqrt(n);
	return s * s == n || (s + 1) * (s + 1) == n;
}
template <class T = long long> inline T BIT(int b) {
	return T(1) << b;
}
template <class T, class U = typename T::value_type> inline U Gcdv(const T& v) {
	return accumulate(next(v.begin()), v.end(), U(*v.begin()), gcd<U, U>);
}
template <class T, class U = typename T::value_type> inline U Lcmv(const T& v) {
	return accumulate(next(v.begin()), v.end(), U(*v.begin()), lcm<U, U>);
}
template <class T> inline T Pow(T a, T n) {
	T r = 1;
	while (n > 0) {
		if (n & 1) r *= a;
		a *= a;
		n /= 2;
	}
	return r;
}
template <class T> inline T Powmod(T a, T n, T m = MOD) {
	T r = 1;
	while (n > 0) {
		if (n & 1)
			r = r * a % m, n--;
		else
			a = a * a % m, n /= 2;
	}
	return r;
}
#line 9 "/home/yuruhiya/programming/library/template/template.cpp"
#if __has_include(<library/dump.hpp>)
#include <library/dump.hpp>
#define LOCAL
#else
#define dump(...) ((void)0)
#endif

template <class T> constexpr T oj_local(const T& oj, const T& local) {
#ifndef LOCAL
	return oj;
#else
	return local;
#endif
}
#line 5 "/home/yuruhiya/programming/library/Geometry/Geometric.hpp"
#include <optional>
using namespace std;

namespace Geometric {

	using LD = long double;
	constexpr long double PI = 3.14159265358979323846, EPS = 1e-12;

	constexpr bool Equal(LD a, LD b);
	// a > 0 : +1
	// a = 0 :  0
	// a < 0 : -1
	constexpr int sgn(LD a);
	constexpr LD deg_to_rad(LD deg);
	constexpr LD rad_to_deg(LD rad);

	struct Vec2;
	struct Line;
	struct Segment;
	struct Rect;
	struct Circle;
	struct Polygon;

	// AB から見て BC が左に曲がる   : +1
	// AB から見て BC が右に曲がる   : -1
	// ABC, CBA の順に一直線上に並ぶ : +2
	// ACB, BCA の順に一直線上に並ぶ :  0
	// BAC, CAB の順に一直線上に並ぶ : -2
	int iSP(const Vec2& a, const Vec2& b, const Vec2& c);

	// 角ABC が鋭角 : 0, 直角 : 1, 鈍角 : 2
	int angle_type(const Vec2& a, const Vec2& b, const Vec2& c);

	// 距離
	LD distance(const Vec2& v1, const Vec2& v2);
	LD distance(const Vec2& v, const Line& l);
	LD distance(const Vec2& v, const Segment& s);
	LD distance(const Vec2& v, const Circle& c);
	LD distance(const Line& l, const Vec2& v);
	LD distance(const Line& l1, const Line& l2);
	LD distance(const Segment& s, const Vec2& v);
	LD distance(const Segment& s1, const Segment& s2);
	LD distance(const Circle& c, const Vec2& v);
	LD distance(const Circle& c1, const Circle& c2);

	// 交差判定 （内包しているときも true を返す）
	bool intersect(const Vec2& v1, const Vec2& v2);
	bool intersect(const Vec2& v, const Line& l);
	bool intersect(const Vec2& v, const Segment& l);
	bool intersect(const Vec2& v, const Circle& c);
	bool intersect(const Vec2& v, const Rect& r);
	bool intersect(const Line& l, const Vec2& v);
	bool intersect(const Line& l1, const Line& l2);
	bool intersect(const Line& l, const Circle& c);
	bool intersect(const Segment& l, const Vec2& v);
	bool intersect(const Segment& s1, const Segment& s2);
	bool intersect(const Segment& s, const Circle& c);
	bool intersect(const Circle& c, const Vec2& v);
	bool intersect(const Circle& c, const Line& l);
	bool intersect(const Circle& c, const Segment& s);
	bool intersect(const Circle& c1, const Circle& c2);
	bool intersect(const Circle& c, const Rect& r);
	bool intersect(const Rect& r1, const Rect& r2);
	bool intersect(const Rect& r, const Circle& c);

	// 交点
	optional<Vec2> cross_point(const Line& l1, const Line& l2);
	optional<Vec2> cross_point(const Segment& s1, const Segment& s2);

	vector<Vec2> cross_points(const Line& l, const Circle& c);
	vector<Vec2> cross_points(const Circle& c,const Line& l);
	vector<Vec2> cross_points(const Circle& c1, const Circle& c2);

}  // namespace Geometric
#line 5 "/home/yuruhiya/programming/library/Geometry/Vec2.hpp"

namespace Geometric {

	struct Vec2 {
		LD x, y;
		static bool compare_x(const Vec2& v1, const Vec2& v2) {
			return v1.x < v2.x;
		}
		static bool compare_y(const Vec2& v1, const Vec2& v2) {
			return v1.y < v2.y;
		}
		static bool compare_xy(const Vec2& v1, const Vec2& v2) {
			return make_pair(v1.x, v1.y) < make_pair(v2.x, v2.y);
		}
		static bool compare_yx(const Vec2& v1, const Vec2& v2) {
			return make_pair(v1.y, v1.x) < make_pair(v2.y, v2.x);
		}
		constexpr Vec2() : x(0), y(0) {}
		constexpr Vec2(LD _x, LD _y) : x(_x), y(_y) {}
		Vec2(LD rad) : x(cos(rad)), y(sin(rad)) {}
		constexpr bool operator==(const Vec2& v) const {
			return Equal(x, v.x) && Equal(y, v.y);
		}
		constexpr bool operator!=(const Vec2& v) const {
			return !(*this == v);
		}
		constexpr bool operator<(const Vec2& v) const {
			return x < v.x - EPS && y < v.y - EPS;
		}
		constexpr bool operator<=(const Vec2& v) const {
			return x < v.x + EPS && y < v.y + EPS;
		}
		constexpr Vec2 operator+() const {
			return *this;
		}
		constexpr Vec2 operator-() const {
			return {-x, -y};
		}
		constexpr Vec2 operator+(const Vec2& v) const {
			return Vec2(*this) += v;
		}
		constexpr Vec2 operator-(const Vec2& v) const {
			return Vec2(*this) -= v;
		}
		constexpr Vec2 operator*(const Vec2& v) const {
			return Vec2(*this) *= v;
		}
		constexpr Vec2 operator/(const Vec2& v) const {
			return Vec2(*this) /= v;
		}
		constexpr Vec2 operator+(LD n) const {
			return Vec2(*this) += Vec2(n, n);
		}
		constexpr Vec2 operator-(LD n) const {
			return Vec2(*this) -= Vec2(n, n);
		}
		constexpr Vec2 operator*(LD n) const {
			return Vec2(*this) *= Vec2(n, n);
		}
		constexpr Vec2 operator/(LD n) const {
			return Vec2(*this) /= Vec2(n, n);
		}
		constexpr Vec2& operator+=(const Vec2& v) {
			x += v.x;
			y += v.y;
			return *this;
		}
		constexpr Vec2& operator-=(const Vec2& v) {
			x -= v.x;
			y -= v.y;
			return *this;
		}
		constexpr Vec2& operator*=(const Vec2& v) {
			x *= v.x;
			y *= v.y;
			return *this;
		}
		constexpr Vec2& operator/=(const Vec2& v) {
			x /= v.x;
			y /= v.y;
			return *this;
		}
		constexpr Vec2& operator+=(LD n) {
			x += n;
			x += n;
			return *this;
		}
		constexpr Vec2& operator-=(LD n) {
			x -= n;
			x -= n;
			return *this;
		}
		constexpr Vec2& operator*=(LD n) {
			x *= n;
			x *= n;
			return *this;
		}
		constexpr Vec2& operator/=(LD n) {
			x /= n;
			x /= n;
			return *this;
		}
		constexpr LD operator[](size_t i) const {
			return i == 0 ? x : i == 1 ? y : 0;
		}
		LD manhattan(const Vec2& v) const {
			return std::abs(x - v.x) + std::abs(y - v.y);
		}
		template <class Shape2DType> LD distance(const Shape2DType& shape) const {
			return Geometric::distance(*this, shape);
		}
		template <class Shape2DType> bool intersects(const Shape2DType& shape) const {
			return Geometric::intersect(*this, shape);
		}
		constexpr LD length_square() const {
			return dot(*this);
		}
		LD length() const {
			return sqrt(length_square());
		}
		// 内積
		constexpr LD dot(const Vec2& v) const {
			return x * v.x + y * v.y;
		}
		// 外積
		constexpr LD cross(const Vec2& v) const {
			return x * v.y - y * v.x;
		}
		// 正規化（長さを1にした）ベクトル
		Vec2 normalized() const {
			return *this / length();
		}
		// 原点中心に rad 回転した座標
		Vec2 rotation(LD rad) const {
			LD c = cos(rad), s = sin(rad);
			return {x * c - y * s, x * s + y * c};
		}
		// 原点中心の円上に乗っているとしたときの偏角
		LD angle() const {
			return atan2(y, x);
		}
		// 正射影
		Vec2 projection(const Line& l) const;
		// 鏡映変換
		Vec2 reflection(const Line& l) const;
		constexpr Vec2 rotate90() const {
			return {y, -x};
		}
		constexpr Vec2 rotate180() const {
			return {-x, -y};
		}
		constexpr Vec2 rotate270() const {
			return {-y, x};
		}
		friend ostream& operator<<(ostream& os, const Vec2& v) {
			return os << '(' << v.x << ", " << v.y << ')';
		}
		friend istream& operator>>(istream& is, Vec2& v) {
			return is >> v.x >> v.y;
		}
	};

}  // namespace Geometric
#line 9 "/home/yuruhiya/programming/library/Geometry/Polygon.hpp"
using namespace std;

namespace Geometric {

	struct Polygon : vector<Vec2> {
	public:
		Polygon(int n) : vector<Vec2>(n) {}
		Polygon(const vector<Vec2>& _p) : vector<Vec2>(_p) {}
		LD area() const {
			LD ans = 0;
			for (size_t i = 0; i < size(); ++i) {
				size_t next = i < size() - 1 ? i : 0;
				ans += abs(at(i).x * at(i).y - at(next).x * at(i).y);
			}
			return ans / 2;
		}
		// 凸性判定（反時計回り）
		bool is_convex() const {
			if (size() < 3) {
				return false;
			}
			for (size_t i = 0; i < size(); ++i) {
				size_t prev = i != 0 ? i - 1 : size() - 1;
				size_t next = i != size() - 1 ? i + 1 : 0;
				if (iSP(at(prev), at(i), at(next)) == -1) {
					return false;
				}
			}
			return true;
		}
		// 凸包（反時計回り）
		Polygon convex_hull() const {
			vector<Vec2> ps = *this;
			sort(ps.begin(), ps.end(), [](const Vec2& v1, const Vec2& v2) {
				return make_pair(v1.x, v1.y) < make_pair(v2.x, v2.y);
			});
			int n = ps.size(), k = 0;
			Polygon res(2 * n);
			for (int i = 0; i < n; res[k++] = ps[i++]) {
				while (k >= 2 && iSP(res[k - 2], res[k - 1], ps[i]) <= 0) {
					--k;
				}
			}
			for (int i = n - 2, t = k + 1; i >= 0; res[k++] = ps[i--]) {
				while (k >= t && iSP(res[k - 2], res[k - 1], ps[i]) <= 0) {
					--k;
				}
			}
			res.resize(k - 1);
			return res;
		}
		// 凸包（一直線上の3点を含めない、反時計回り）
		Polygon convex_hull_no_collinear() const {
			vector<Vec2> ps = *this;
			sort(ps.begin(), ps.end(), [](const Vec2& v1, const Vec2& v2) {
				return make_pair(v1.x, v1.y) < make_pair(v2.x, v2.y);
			});
			int n = ps.size(), k = 0;
			Polygon res(2 * n);
			for (int i = 0; i < n; res[k++] = ps[i++]) {
				while (k >= 2 && iSP(res[k - 2], res[k - 1], ps[i]) != -1) {
					--k;
				}
			}
			for (int i = n - 2, t = k + 1; i >= 0; res[k++] = ps[i--]) {
				while (k >= t && iSP(res[k - 2], res[k - 1], ps[i]) != -1) {
					--k;
				}
			}
			res.resize(k - 1);
			return res;
		}
		// 直径
		tuple<LD, size_t, size_t> diameter() const {
			size_t i_start = 0, j_start = 0;
			for (size_t i = 1; i < size(); ++i) {
				if (at(i).y > at(i_start).y) i_start = i;
				if (at(i).y < at(j_start).y) j_start = i;
			}
			LD max_dist = (at(i_start) - at(j_start)).length();

			auto diff = [&](int i) {
				return at((i + 1) % size()) - at(i);
			};

			size_t i = i_start, i_max = i_start;
			size_t j = j_start, j_max = j_start;
			do {
				if (diff(i).cross(diff(j)) >= 0) {
					j = (j + 1) % size();
				} else {
					i = (i + 1) % size();
				}
				if (LD d = (at(i) - at(j)).length(); max_dist < d) {
					max_dist = d;
					i_max = i;
					j_max = j;
				}
			} while (i != i_start || j != j_start);
			return {max_dist, i_max, j_max};
		}
		// 最近点対
		tuple<LD, Vec2, Vec2> closest_pair() const {
			vector<Vec2> points = *this;
			sort(points.begin(), points.end(), Vec2::compare_xy);

			auto dfs = [&](auto self, int left, int right) -> tuple<LD, Vec2, Vec2> {
				int n = right - left;
				if (n <= 1) {
					return {1e64, points[left], points[left]};
				} else {
					int mid = (left + right) / 2;
					LD x = points[mid].x;
					auto res = min(self(self, left, mid), self(self, mid, right));
					inplace_merge(points.begin() + left, points.begin() + mid, points.begin() + right, Vec2::compare_y);

					vector<Vec2> around;
					for (int i = left; i < right; ++i) {
						if (get<0>(res) <= abs(points[i].x - x)) {
							continue;
						}
						for (int size = around.size(), j = size - 1; j >= 0; --j) {
							if (get<0>(res) <= points[i].y - around[j].y) {
								break;
							}
							if (LD length = (points[i] - around[j]).length(); get<0>(res) > length) {
								res = {length, points[i], around[j]};
							}
						}
						around.push_back(points[i]);
					}
					return res;
				}
			};

			return dfs(dfs, 0, size());
		}

		friend ostream& operator<<(ostream& os, const Polygon& p) {
			os << "{ ";
			for (size_t i = 0; i < p.size(); ++i) {
				if (i != 0) os << ", ";
				os << p[i];
			}
			return os << " }";
		}
		friend istream& operator>>(istream& is, Polygon& p) {
			for (auto& v : p) {
				is >> v;
			}
			return is;
		}
	};

}  // namespace Geometric
#line 9 "/home/yuruhiya/programming/library/Geometry/Line.hpp"
using namespace std;

namespace Geometric {

	namespace internal {
		struct LineBase {
		protected:
			constexpr LineBase() = default;
			constexpr LineBase(const Vec2& _begin, const Vec2& _end) : begin(_begin), end(_end) {}
			constexpr LineBase(LD begin_x, LD begin_y, LD end_x, LD end_y)
			    : begin(begin_x, begin_y), end(end_x, end_y) {}

		public:
			Vec2 begin, end;
			constexpr Vec2 vec() const {
				return end - begin;
			}
			constexpr Vec2 counter_vec() const {
				return begin - end;
			}
			// 平行判定
			constexpr bool is_parallel(const LineBase& l) const {
				return sgn(vec().cross(l.vec())) == 0;
			}
			// 直交判定
			constexpr bool is_orthogonal(const LineBase& l) const {
				return sgn(vec().dot(l.vec())) == 0;
			}
			friend ostream& operator<<(ostream& os, const LineBase& l) {
				return os << '(' << l.begin << ", " << l.end << ')';
			}
			friend istream& operator>>(istream& is, LineBase& l) {
				return is >> l.begin >> l.end;
			}
		};
	}  // namespace internal

	struct Line : internal::LineBase {
		Line() = default;
		Line(const Vec2& _begin, const Vec2& _end) : LineBase(_begin, _end) {}
		constexpr Line(LD begin_x, LD begin_y, LD end_x, LD end_y) : LineBase(begin_x, begin_y, end_x, end_y) {}
		Line(const LineBase& l) : LineBase(l) {}
		template <class Shape2DType> LD distance(const Shape2DType& shape) const {
			return Geometric::distance(*this, shape);
		}
		template <class Shape2DType> bool intersects(const Shape2DType& shape) const {
			return Geometric::intersect(*this, shape);
		}
		template <class Shape2DType> optional<Vec2> cross_point(const Shape2DType& shape) const {
			return Geometric::cross_point(*this, shape);
		}
		template <class Shape2DType> vector<Vec2> cross_points(const Shape2DType& shape) const {
			return Geometric::cross_points(*this, shape);
		}
		// ax + by + c = 0 の式に変形する
		tuple<LD, LD, LD> abc() const {
			if (sgn(begin.x - end.x) == 0) {
				return {1, 0, -begin.x};
			} else {
				LD slope = (end.y - begin.y) / (end.x - begin.x);
				return {slope, -1, begin.y - begin.x * slope};
			}
		}
	};

	struct Segment : internal::LineBase {
		Segment() = default;
		Segment(const Vec2& _begin, const Vec2& _end) : LineBase(_begin, _end) {}
		constexpr Segment(LD begin_x, LD begin_y, LD end_x, LD end_y) : LineBase(begin_x, begin_y, end_x, end_y) {}
		Segment(const LineBase& l) : LineBase(l) {}
		template <class Shape2DType> LD distance(const Shape2DType& shape) const {
			return Geometric::distance(*this, shape);
		}
		template <class Shape2DType> bool intersects(const Shape2DType& shape) const {
			return Geometric::intersect(*this, shape);
		}
		template <class Shape2DType> optional<Vec2> cross_point(const Shape2DType& shape) const {
			return Geometric::cross_point(*this, shape);
		}
		template <class Shape2DType> vector<Vec2> cross_points(const Shape2DType& shape) const {
			return Geometric::cross_points(*this, shape);
		}
	};

}  // namespace Geometric
#line 6 "/home/yuruhiya/programming/library/Geometry/Circle.hpp"
using namespace std;

namespace Geometric {

	struct Circle {
		Vec2 center;
		LD r;
		constexpr Circle() : center(), r(0) {}
		constexpr Circle(LD _r) : center(), r(_r) {}
		constexpr Circle(LD _x, LD _y, LD _r) : center(_x, _y), r(_r) {}
		constexpr Circle(const Vec2& _c, LD _r) : center(_c), r(_r) {}
		constexpr bool operator==(const Circle& c) const {
			return center == c.center && Equal(r, c.r);
		}
		constexpr bool operator!=(const Circle& c) const {
			return !(*this == c);
		}
		constexpr Circle& operator+(const Vec2& v) const {
			return Circle(*this) += v;
		}
		constexpr Circle& operator-(const Vec2& v) const {
			return Circle(*this) -= v;
		}
		constexpr Circle& operator+=(const Vec2& v) {
			center += v;
			return *this;
		}
		constexpr Circle& operator-=(const Vec2& v) {
			center -= v;
			return *this;
		}
		constexpr LD top_y() const {
			return center.y - r;
		}
		constexpr LD bottom_y() const {
			return center.y + r;
		}
		constexpr LD left_x() const {
			return center.x - r;
		}
		constexpr LD right_x() const {
			return center.x + r;
		}
		constexpr Vec2 top() const {
			return center - Vec2(0, r);
		}
		constexpr Vec2 bottom() const {
			return center + Vec2(0, r);
		}
		constexpr Vec2 left() const {
			return center - Vec2(r, 0);
		}
		constexpr Vec2 right() const {
			return center + Vec2(r, 0);
		}
		constexpr LD area() const {
			return r * r * PI;
		}
		constexpr LD perimeter() const {
			return 2 * r * PI;
		}
		template <class Shape2DType> LD distance(const Shape2DType& shape) const {
			return Geometric::distance(*this, shape);
		}
		template <class Shape2DType> bool intersects(const Shape2DType& shape) const {
			return Geometric::intersect(*this, shape);
		}
		template <class Shape2DType> vector<Vec2> cross_points(const Shape2DType& shape) const {
			return Geometric::cross_points(*this, shape);
		}
		bool contains(const Circle& c) const {
			return center.distance(c.center) + c.r < r - EPS;
		}
		bool tangent(const Circle& c) const {
			LD l1 = center.distance(c.center), l2 = r, l3 = c.r;
			return Equal(l1 + l2 + l3, max({l1, l2, l3}) * 2);
		}
		friend ostream& operator<<(ostream& os, const Circle& c) {
			return os << '(' << c.center.x << ',' << c.center.y << ',' << c.r << ')';
		}
		friend istream& operator>>(istream& is, Circle& c) {
			return is >> c.center >> c.r;
		}
	};

}  // namespace Geometric
#line 5 "/home/yuruhiya/programming/library/Geometry/Rect.hpp"
using namespace std;

namespace Geometric {

	struct Rect {
		Vec2 pos, size;
		constexpr Rect() {}
		constexpr Rect(LD _w, LD _h) : size(_w, _h) {}
		constexpr Rect(const Vec2& _size) : size(_size) {}
		constexpr Rect(LD _x, LD _y, LD _w, LD _h) : pos(_x, _y), size(_w, _h) {}
		constexpr Rect(const Vec2& _pos, const Vec2& _size) : pos(_pos), size(_size) {}
		constexpr bool operator==(const Rect& r) const {
			return pos == r.pos && size == r.size;
		}
		constexpr bool operator!=(const Rect& r) const {
			return !(*this == r);
		}
		constexpr Rect operator+(const Vec2& v) const {
			return Rect(*this) += v;
		}
		constexpr Rect operator-(const Vec2& v) const {
			return Rect(*this) -= v;
		}
		constexpr Rect& operator+=(const Vec2& v) {
			pos += v;
			return *this;
		}
		constexpr Rect& operator-=(const Vec2& v) {
			pos -= v;
			return *this;
		}
		constexpr Rect& set_center(const Vec2& _pos) {
			pos = _pos - size / 2;
			return *this;
		}
		constexpr LD left() const {
			return pos.x;
		}
		constexpr LD right() const {
			return pos.x + size.x;
		}
		constexpr LD top() const {
			return pos.y;
		}
		constexpr LD bottom() const {
			return pos.y + size.y;
		}
		constexpr Vec2 top_left() const {
			return pos;
		}
		constexpr Vec2 top_right() const {
			return pos + Vec2(size.x, 0);
		}
		constexpr Vec2 bottom_left() const {
			return pos + Vec2(0, size.y);
		}
		constexpr Vec2 bottom_right() const {
			return pos + size;
		}
		constexpr Vec2 center() const {
			return pos + size / 2;
		}
		constexpr LD area() const {
			return size.x * size.y;
		}
		constexpr LD perimeter() const {
			return (size.x + size.y) * 2;
		}
		template <class Shape2DType> LD distance(const Shape2DType& shape) const {
			return Geometric::distance(*this, shape);
		}
		template <class Shape2DType> bool intersects(const Shape2DType& shape) const {
			return Geometric::intersect(*this, shape);
		}
		constexpr bool contains(const Rect& r) const {
			return top_left() <= r.top_left() && r.bottom_right() <= bottom_right();
		}
		constexpr bool contains(const Circle& c) const {
			return top_left() <= Vec2(c.left_x(), c.top_y()) && Vec2(c.right_x(), c.bottom_y()) <= bottom_right();
		}
		friend ostream& operator<<(ostream& os, const Rect& r) {
			return os << '(' << r.pos << ',' << r.size << ')';
		}
		friend istream& operator>>(istream& is, Rect& r) {
			return is >> r.pos >> r.size;
		}
	};

}  // namespace Geometric
#line 8 "/home/yuruhiya/programming/library/Geometry/Triangle.hpp"
using namespace std;

namespace Geometric {

	struct Triangle {
		Vec2 p1, p2, p3;
		static LD area(LD a, LD b, LD c) {
			LD s = (a + b + c) / 2;
			return sqrt(s * (s - a) * (s - b) * (s - c));
		}
		Triangle() = default;
		Triangle(const Vec2& _p1, const Vec2& _p2, const Vec2& _p3) : p1(_p1), p2(_p2), p3(_p3) {
			assert(abs(iSP(p1, p2, p3)) == 1);
		}
		tuple<LD, LD, LD> sides() const {
			return {p2.distance(p3), p1.distance(p3), p1.distance(p2)};
		}
		LD area() const {
			auto [l1, l2, l3] = sides();
			return area(l1, l2, l3);
		}
		// 内接円
		Circle incircle() const {
			auto [l1, l2, l3] = sides();
			LD s = l1 + l2 + l3;
			LD x = (p1.x * l1 + p2.x * l2 + p3.x * l3) / s;
			LD y = (p1.y * l1 + p2.y * l2 + p3.y * l3) / s;
			s /= 2;
			LD r = sqrt((s - l1) * (s - l2) * (s - l3) / s);
			return Circle(x, y, r);
		}
		// 外接円
		Circle cirnumscribed_circle() const {
			Line l1((p1 + p2) / 2, (p1 + p2) / 2 + (p1 - p2).rotate270());
			Line l2((p1 + p3) / 2, (p1 + p3) / 2 + (p1 - p3).rotate270());
			Vec2 center = *l1.cross_point(l2);
			return Circle(center, center.distance(p1));
		}
		friend ostream& operator<<(ostream& os, const Triangle& t) {
			return os << '(' << t.p1 << ", " << t.p2 << ", " << t.p3 << ')';
		}
		friend istream& operator>>(istream& is, Triangle& t) {
			return is >> t.p1 >> t.p2 >> t.p3;
		}
	};

}  // namespace Geometric
#line 8 "/home/yuruhiya/programming/library/Geometry/Geometric.cpp"

namespace Geometric {

	constexpr bool Equal(LD a, LD b) {
		return a < b ? b - a < EPS : a - b < EPS;
	}
	// a > 0  : +1
	// a == 0 :  0
	// a < 0  : -1
	constexpr int sgn(LD a) {
		return a < -EPS ? -1 : a > EPS ? 1 : 0;
	}

	constexpr LD deg_to_rad(LD deg) {
		return deg * PI / 180;
	}
	constexpr LD rad_to_deg(LD rad) {
		return rad * 180 / PI;
	}

	Vec2 Vec2::projection(const Line& l) const {
		return l.begin + l.vec().normalized() * (*this - l.begin).dot(l.vec()) / l.vec().length();
	}
	Vec2 Vec2::reflection(const Line& l) const {
		return *this + (projection(l) - *this) * 2;
	}

	int iSP(const Vec2& a, const Vec2& b, const Vec2& c) {
		int flag = sgn((b - a).cross(c - a));
		if (flag != 0) {
			return flag;
		} else {
			if (sgn((b - a).dot(c - b)) > 0) {
				return 2;
			} else if (sgn((a - b).dot(c - a)) > 0) {
				return -2;
			} else {
				return 0;
			}
		}
	}

	int angle_type(const Vec2& a, const Vec2& b, const Vec2& c) {
		if (int f = sgn((a - b).dot(c - b)); f > 0) {
			return 0;
		} else if (f == 0) {
			return 1;
		} else {
			return 2;
		}
	}

	LD distance(const Vec2& v1, const Vec2& v2) {
		return hypot(v1.x - v2.x, v1.y - v2.y);
	}
	LD distance(const Vec2& v, const Line& l) {
		return abs(l.vec().cross(v - l.begin) / l.vec().length());
	}
	LD distance(const Vec2& v, const Segment& s) {
		if (sgn(s.vec().dot(v - s.begin)) < 0 || sgn(s.counter_vec().dot(v - s.end)) < 0) {
			return min(v.distance(s.begin), v.distance(s.end));
		} else {
			return Line(s).distance(v);
		}
	}
	LD distance(const Vec2& v, const Circle& c) {
		return max<LD>(0, c.center.distance(v) - c.r);
	}
	LD distance(const Line& l, const Vec2& v) {
		return distance(v, l);
	}
	LD distance(const Line& l1, const Line& l2) {
		return l1.is_parallel(l2) ? l1.distance(l2.begin) : 0;
	}
	LD distance(const Segment& s, const Vec2& v) {
		return distance(v, s);
	}
	LD distance(const Segment& s1, const Segment& s2) {
		if (intersect(s1, s2)) {
			return 0;
		} else {
			return min({distance(s1, s2.begin), distance(s1, s2.end), distance(s1.begin, s2), distance(s1.end, s2)});
		}
	}
	LD distance(const Circle& c, const Vec2& v) {
		return distance(v, c);
	}
	LD distance(const Circle& c1, const Circle& c2) {
		return max<LD>(0, distance(c1.center, c2.center) - (c1.r + c2.r));
	}

	bool intersect(const Vec2& v1, const Vec2& v2) {
		return v1 == v2;
	}
	bool intersect(const Vec2& v, const Line& l) {
		return abs(iSP(v, l.begin, l.end)) != -1;
	}
	bool intersect(const Vec2& v, const Segment& l) {
		return iSP(l.begin, l.end, v) == 0;
	}
	bool intersect(const Vec2& v, const Circle& c) {
		return c.center.distance(v) < c.r + EPS;
	}
	bool intersect(const Vec2& v, const Rect& r) {
		return r.pos <= v && v <= r.bottom_right();
	}
	bool intersect(const Line& l, const Vec2& v) {
		return intersect(v, l);
	}
	bool intersect(const Line& l1, const Line& l2) {
		return !l1.is_parallel(l2);
	}
	bool intersect(const Line& l, const Circle& c) {
		return sgn(distance(c.center, l) - c.r) <= 0;
	}
	bool intersect(const Segment& l, const Vec2& v) {
		return intersect(v, l);
	}
	bool intersect(const Segment& s1, const Segment& s2) {
		return iSP(s1.begin, s1.end, s2.begin) * iSP(s1.begin, s1.end, s2.end) <= 0 &&
		    iSP(s2.begin, s2.end, s1.begin) * iSP(s2.begin, s2.end, s1.end) <= 0;
	}
	bool intersect(const Segment& s, const Circle& c) {
		return sgn(distance(c.center, s) - c.r) <= 0;
	}
	bool intersect(const Circle& c, const Vec2& v) {
		return intersect(v, c);
	}
	bool intersect(const Circle& c, const Line& l) {
		return intersect(l, c);
	}
	bool intersect(const Circle& c, const Segment& s) {
		return intersect(s, c);
	}
	bool intersect(const Circle& c1, const Circle& c2) {
		return sgn(distance(c1.center, c2.center) - (c1.r + c2.r)) <= 0;
	}
	bool intersect(const Circle& c, const Rect& r) {
		return Rect(r.pos - Vec2(0, c.r), r.size + Vec2(0, c.r * 2)).intersects(c.center) ||
		    Rect(r.pos - Vec2(c.r, 0), r.size + Vec2(c.r * 2, 0)).intersects(c.center) || c.intersects(r.top_left()) ||
		    c.intersects(r.top_right()) || c.intersects(r.bottom_left()) || c.intersects(r.bottom_right());
	}
	bool intersect(const Rect& r1, const Rect& r2) {
		return max(r1.left(), r2.left()) < min(r1.right(), r2.right()) + EPS &&
		    max(r1.top(), r2.top()) < min(r1.bottom(), r2.bottom()) + EPS;
	}
	bool intersect(const Rect& r, const Circle& c) {
		return intersect(c, r);
	}

	optional<Vec2> cross_point(const Line& l1, const Line& l2) {
		if (intersect(l1, l2)) {
			// return begin + vec() * abs((l.end - begin).cross(l.vec()) / vec().cross(l.vec()));
			auto [a, b, c] = l1.abc();
			auto [A, B, C] = l2.abc();
			LD d = A * b - a * B;
			return Vec2((B * c - b * C) / d, (a * C - A * c) / d);
		} else {
			return nullopt;
		}
	}
	optional<Vec2> cross_point(const Segment& s1, const Segment& s2) {
		if (intersect(s1, s2)) {
			return cross_point(Line(s1), Line(s2));
		} else {
			return nullopt;
		}
	}

	vector<Vec2> cross_points(const Line& l, const Circle& c) {
		LD dist = distance(l, c.center);
		if (int f = sgn(c.r - dist); f == 1) {
			LD x = sqrt(c.r * c.r - dist * dist);
			Vec2 p = c.center.projection(l);
			return {p + l.vec().normalized() * x, p + l.counter_vec().normalized() * x};
		} else if (f == 0) {
			return {c.center.projection(l)};
		} else {
			return {};
		}
	}
	vector<Vec2> cross_points(const Circle& c, const Line& l) {
		return cross_points(l, c);
	}
	vector<Vec2> cross_points(const Circle& c1, const Circle& c2) {
		Vec2 vec = (c1.center - c2.center).normalized();  // c2 -> c1
		LD dist = c1.center.distance(c2.center);
		if (c1.contains(c2) || c2.contains(c1)) {
			return {};
		} else if (sgn(dist - c1.r - c2.r) == 0) {
			return {c2.center + vec * c2.r};
		} else if (sgn(c1.r + dist - c2.r) == 0) {
			return {c1.center + vec * c1.r};
		} else if (sgn(c2.r + dist - c1.r) == 0) {
			return {c2.center + vec.rotate180() * c2.r};
		} else if (intersect(c1, c2)) {
			LD area = Triangle::area(dist, c1.r, c2.r);
			LD y = 2 * area / dist, x = sqrt(c1.r * c1.r - y * y);
			LD r1_s = c1.r * c1.r, r2_s = c2.r * c2.r, dist_s = dist * dist;
			Vec2 h = c1.center + vec * (r2_s < r1_s + dist_s ? -x : x), v2 = vec.rotate90() * y;
			return {h + v2, h - v2};
		} else {
			return {};
		}
	}

}  // namespace Geometric
#line 4 "a.cpp"

int main() {
	Geometric::Polygon p(5);
	rep(i, 5) in(p[i]);
	do {
		if (p.convex_hull_no_collinear().size() == 5) {
			dump(p.convex_hull_no_collinear());
			out.exit("YES");
		}
	} while (next_permutation(all(p)));
	out("NO");
}