#line 1 "a.cpp"
#line 2 "/home/nok0/documents/programming/library/template/header.hpp"
#include <bits/stdc++.h>
#line 3 "/home/nok0/documents/programming/library/template/def_const.hpp"

const int inf = 1000000000;
const long long INF = 1000000000000000000ll;
#line 4 "/home/nok0/documents/programming/library/template/debug.hpp"

namespace viewer {
void view(const long long &e) {
	if(e == INF)
		std::cerr << "INF";
	else if(e == -INF)
		std::cerr << "-INF";
	else
		std::cerr << e;
}

void view(const int &e) {
	if(e == inf)
		std::cerr << "inf";
	else if(e == -inf)
		std::cerr << "-inf";
	else
		std::cerr << e;
}

template <typename T>
void view(const T &e) {
	std::cerr << e;
}

template <typename T, typename U>
void view(const std::pair<T, U> &p) {
	std::cerr << "(";
	view(p.first);
	std::cerr << ", ";
	view(p.second);
	std::cerr << ")";
}

template <class T0, class T1, class T2>
void view(const std::tuple<T0, T1, T2> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ")";
}

template <class T0, class T1, class T2, class T3>
void view(const std::tuple<T0, T1, T2, T3> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ", ";
	view(std::get<3>(p));
	std::cerr << ")";
}

template <typename T>
void view(const std::set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::unordered_set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::multiset<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::unordered_multiset<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<T> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(const auto &e : v) {
		view(e);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T, std::size_t ary_size>
void view(const std::array<T, ary_size> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(const auto &e : v) {
		view(e);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<std::vector<T>> &vv) {
	std::cerr << "{\n";
	for(const auto &v : vv) {
		std::cerr << "\t";
		view(v);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::vector<std::pair<T, U>> &v) {
	std::cerr << "{\n";
	for(const auto &c : v) {
		std::cerr << "\t(";
		view(c.first);
		std::cerr << ", ";
		view(c.second);
		std::cerr << ")\n";
	}
	std::cerr << "}";
}

template <class T0, class T1, class T2>
void view(const std::vector<std::tuple<T0, T1, T2>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <class T0, class T1, class T2, class T3>
void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <typename T, typename U>
void view(const std::map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::unordered_map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}
}  // namespace viewer

// when compiling : g++ foo.cpp -DLOCAL
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	viewer::view(H);
	std::cerr << ", ";
	debug_out(T...);
}
#define debug(...)                                                \
	do {                                                          \
		std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
		debug_out(__VA_ARGS__);                                   \
		std::cerr << "\b\b]\n";                                   \
	} while(0)
#define dump(x)                                      \
	do {                                             \
		std::cerr << __LINE__ << " " << #x << " : "; \
		viewer::view(x);                             \
		std::cerr << '\n';                           \
	} while(0)

#else
#define debug(...) (void(0))
#define dump(x)    (void(0))
#endif
#line 3 "/home/nok0/documents/programming/library/template/def_name.hpp"

#define pb        push_back
#define eb        emplace_back
#define SZ(x)     ((int)(x).size())
#define all(x)    (x).begin(), (x).end()
#define rall(x)   (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template <class T = int>
using V = std::vector<T>;
template <class T = int>
using VV = std::vector<std::vector<T>>;
template <class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
#line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp"

struct fast_io {
	fast_io() {
		std::ios::sync_with_stdio(false);
		std::cin.tie(nullptr);
		std::cout << std::fixed << std::setprecision(15);
	}
} fast_io_;
#line 3 "/home/nok0/documents/programming/library/template/input.hpp"

template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
	is >> p.first >> p.second;
	return is;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
	for(T &i : v) is >> i;
	return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
	std::string s;
	is >> s;
	__int128_t ret = 0;
	for(int i = 0; i < (int)s.length(); i++)
		if('0' <= s[i] and s[i] <= '9')
			ret = 10 * ret + s[i] - '0';
	a = ret * (s[0] == '-' ? -1 : 1);
	return is;
}
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template <class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template <class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &...tail) {
	scan(head);
	INPUT(tail...);
}
}  // namespace scanner
#define VEC(type, name, size)     \
	std::vector<type> name(size); \
	scanner::INPUT(name)
#define VVEC(type, name, h, w)                                    \
	std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
	scanner::INPUT(name)
#define INT(...)     \
	int __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LL(...)            \
	long long __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define STR(...)             \
	std::string __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define CHAR(...)     \
	char __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...)     \
	double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LD(...)              \
	long double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#line 3 "/home/nok0/documents/programming/library/template/math.hpp"

template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
	T ret = 1;
	while(n) {
		if(n & 1) ret *= a;
		a *= a;
		n >>= 1;
	}
	return ret;
}
long long POW(long long a, long long n, const int mod) {
	long long ret = 1;
	a = (a % mod + mod) % mod;
	while(n) {
		if(n & 1) (ret *= a) %= mod;
		(a *= a) %= mod;
		n >>= 1;
	}
	return ret;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f) {
	while(abs(ok - ng) > 1) {
		T mid = (ok + ng) >> 1;
		(f(mid) ? ok : ng) = mid;
	}
	return ok;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f, int loop) {
	for(int i = 0; i < loop; i++) {
		T mid = (ok + ng) / 2;
		(f(mid) ? ok : ng) = mid;
	}
	return ok;
}
#line 3 "/home/nok0/documents/programming/library/template/output.hpp"


template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
	for(int i = 0; i < int(a.size()); ++i) {
		if(i) os << " ";
		os << a[i];
	}
	return os;
}
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;
}
template <class T>
void print(const T a) { std::cout << a << '\n'; }
template <class Head, class... Tail>
void print(Head H, Tail... T) {
	std::cout << H << ' ';
	print(T...);
}
template <class T>
void printel(const T a) { std::cout << a << '\n'; }
template <class T>
void printel(const std::vector<T> &a) {
	for(const auto &v : a)
		std::cout << v << '\n';
}
template <class Head, class... Tail>
void printel(Head H, Tail... T) {
	std::cout << H << '\n';
	printel(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
#line 2 "/home/nok0/documents/programming/library/template/rep.hpp"

#define foa(v, a)                   for(auto &v : a)
#define repname(a, b, c, d, e, ...) e
#define rep(...)                    repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)
#define rep0(x)                     for(int rep_counter = 0; rep_counter < (x); ++rep_counter)
#define rep1(i, x)                  for(int i = 0; i < (x); ++i)
#define rep2(i, l, r)               for(int i = (l); i < (r); ++i)
#define rep3(i, l, r, c)            for(int i = (l); i < (r); i += (c))

#define repsname(a, b, c, ...) c
#define reps(...)              repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__)
#define reps0(x)               for(int reps_counter = 1; reps_counter <= (x); ++reps_counter)
#define reps1(i, x)            for(int i = 1; i <= (x); ++i)

#define rrepname(a, b, c, ...) c
#define rrep(...)              rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__)
#define rrep0(x)               for(int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter)
#define rrep1(i, x)            for(int i = (x)-1; i >= 0; --i)
#line 3 "/home/nok0/documents/programming/library/template/vector.hpp"

template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
	std::sort(a.begin(), a.end());
	a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
	auto res = a;
	UNIQUE(res);
	for(auto &v : a)
		v = lb(res, v);
	return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...)              SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a)               std::sort((a).begin(), (a).end())
#define SORT1(a, c)            std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v -= x;
}
template <class T>
struct cum_vector {
   public:
	cum_vector() = default;
	template <class U>
	cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {
		for(int i = 0; i < (int)vec.size(); i++)
			cum[i + 1] = cum[i] + vec[i];
	}
	T prod(int l, int r) {
		return cum[r] - cum[l];
	}

   private:
	std::vector<T> cum;
};
std::vector<std::pair<char, int>> rle(const std::string &s) {
	const int n = s.size();
	std::vector<std::pair<char, int>> ret;
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and s[l] == s[r]; r++) {}
		ret.emplace_back(s[l], r - l);
		l = r;
	}
	return ret;
}
template <class T>
std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {
	int n = v.size();
	std::vector<std::pair<T, int>> ret;
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and v[l] == v[r]; r++) {}
		ret.emplace_back(v[l], r - l);
		l = r;
	}
	return ret;
}
std::vector<int> iota(int n) {
	std::vector<int> p(n);
	std::iota(p.begin(), p.end(), 0);
	return p;
}
#line 11 "/home/nok0/documents/programming/library/template/all"
using namespace std;
#line 2 "a.cpp"

using R = long double;
using point = std::complex<R>;
using arrow = point;
const R EPS(1e-10), PI(acosl(-1));

inline bool eq(const R &a, const R &b) { return fabsl(b - a) < EPS; }
inline bool same_point(const point &a, const point &b) { return abs(b - a) < EPS; }
/*
    sign of x
    -1: x < 0
     0: x == 0
     1: x > 0
*/
inline int sgn(const R &x) { return fabsl(x) < EPS ? 0 : (x < 0 ? -1 : 1); }
/*
    sign of (a-b)
    -1: a < b
     0: a == b
     1: a > b
*/
inline int compare(const R &a, const R &b) { return eq(a, b) ? 0 : a < b ? -1 :
	                                                                       1; }

std::istream &operator>>(std::istream &is, point &p) {
	R a, b;
	is >> a >> b;
	p = point(a, b);
	return is;
}
std::ostream &operator<<(std::ostream &os, point &p) { return os << '(' << p.real() << ", " << p.imag() << ')'; }

// rotate point 'p' for counter clockwise direction
point rotate(const point &p, const R &theta) {
	return point(cosl(theta) * p.real() - sinl(theta) * p.imag(), sinl(theta) * p.real() + cosl(theta) * p.imag());
}

R radian_to_degree(const R &r) { return (r * 180.0 / PI); }
R degree_to_radian(const R &d) { return (d * PI / 180.0); }

// get angle a-b-c (<pi)
R get_angle(const point &a, const point &b, const point &c) {
	const point v(a - b), w(c - b);
	R theta = fabsl(atan2l(w.imag(), w.real()) - atan2l(v.imag(), v.real()));
	return std::min(theta, 2 * PI - theta);
}

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

struct segment;
struct line {
	point a, b;
	line() = default;
	line(const point &a, const point &b) : a(a), b(b) {}
	// Ax + By + C = 0
	line(const R &A, const R &B, const R &C) {
		if(eq(A, 0)) {
			assert(!eq(B, 0));
			a = point(0, -C / B), b = point(1, -(A + C) / B);
		} else {
			a = point(-C / A, 0), b = point(-(B + C) / A, 1);
		}
	}
	explicit line(const segment &seg);
	friend std::ostream &operator<<(std::ostream &os, line &ln) { return os << '(' << ln.a << " -- " << ln.b << ')'; }
	friend std::istream &operator>>(std::istream &is, line &a) { return is >> a.a >> a.b; }
};
struct segment {
	point a, b;
	segment() = default;
	segment(const point &a, const point &b) : a(a), b(b) {}
	explicit segment(const line &ln) : a(ln.a), b(ln.b) {}
	friend std::ostream &operator<<(std::ostream &os, segment &seg) { return os << '[' << seg.a << " -- " << seg.b << ']'; }
	friend std::istream &operator>>(std::istream &is, segment &a) { return is >> a.a >> a.b; }
};
line::line(const segment &seg) : a(seg.a), b(seg.b) {}

struct circle {
	point center;
	R radius;
	circle() = default;
	circle(const point &center, const R &radius) : center(center), radius(radius) {}
};

using points = std::vector<point>;
using polygon = std::vector<point>;
using segments = std::vector<segment>;
using lines = std::vector<line>;
using circles = std::vector<circle>;

R cross(const point &a, const point &b) { return real(a) * imag(b) - imag(a) * real(b); }
R dot(const point &a, const point &b) { return real(a) * real(b) + imag(a) * imag(b); }

enum CCW {
	ONLINE_FRONT = -2,
	CLOCKWISE = -1,
	ON_SEGMENT = 0,
	COUNTER_CLOCKWISE = 1,
	ONLINE_BACK = 2,
};
int ccw(const point &a, point b, point c) {
	b -= a, c -= a;
	const R crs_b_c = cross(b, c);
	if(crs_b_c > EPS) return CCW::COUNTER_CLOCKWISE;
	if(crs_b_c < -EPS) return CCW::CLOCKWISE;
	if(dot(b, c) < -EPS) return CCW::ONLINE_BACK;
	if(norm(b) + EPS < norm(c)) return CCW::ONLINE_FRONT;
	return CCW::ON_SEGMENT;
}

bool parallel(const arrow &a, const arrow &b) { return eq(cross(a, b), R(0)); }
bool parallel(const line &a, const line &b) { return parallel(a.b - a.a, b.b - b.a); }
bool parallel(const line &a, const segment &b) { return parallel(a.b - a.a, b.b - b.a); }
bool parallel(const segment &a, const line &b) { return parallel(a.b - a.a, b.b - b.a); }
bool parallel(const segment &a, const segment &b) { return parallel(a.b - a.a, b.b - b.a); }

bool orthogonal(const arrow &a, const arrow &b) { return eq(dot(a, b), R(0)); }
bool orthogonal(const line &a, const line &b) { return orthogonal(a.b - a.a, b.b - b.a); }
bool orthogonal(const line &a, const segment &b) { return orthogonal(a.b - a.a, b.b - b.a); }
bool orthogonal(const segment &a, const line &b) { return orthogonal(a.b - a.a, b.b - b.a); }
bool orthogonal(const segment &a, const segment &b) { return orthogonal(a.b - a.a, b.b - b.a); }

point projection(const line &l, const point &p) { return l.a + (l.a - l.b) * dot(p - l.a, l.a - l.b) / norm(l.a - l.b); }
point projection(const segment &s, const point &p) { return projection(line(s), p); }

point reflection(const line &l, const point &p) { return projection(l, p) * R(2) - p; }
point reflection(const segment &s, const point &p) { return projection(line(s), p); }

R distance(const point &p, const point &q);
R distance(const line &l, const point &p);
int number_of_common_tangents(const circle &c1, const circle &c2) {
	const R r1 = std::min(c1.radius, c2.radius), r2 = std::max(c1.radius, c2.radius), d = distance(c1.center, c2.center);
	int com = compare(r1 + r2, d);
	return com == 1 ? compare(d + r1, r2) + 1 : 3 - com;
}

// number of common points (-1: infinite)
int intersect(const line &l, const point &p) { return int(abs(ccw(l.a, l.b, p)) != 1); }
int intersect(const point &p, const line &l) { return intersect(l, p); }
int intersect(const line &l, const line &m) {
	if(intersect(l, m.a) && intersect(l, m.b)) return -1;
	return int(!parallel(l, m));
}
int intersect(const segment &s, const point &p) { return int(ccw(s.a, s.b, p) == CCW::ON_SEGMENT); }
int intersect(const point &p, const segment &s) { return intersect(s, p); }
int intersect(const line &l, const segment &s) {
	if(intersect(l, s.a) && intersect(l, s.b)) return -1;
	return ccw(l.a, l.b, s.a) * ccw(l.a, l.b, s.b) != 1;
}
int intersect(const segment &s, const line &l) { return intersect(l, s); }
int intersect(const circle &c, const line &l) {
	R d = c.radius - distance(l, c.center);
	return fabsl(d) < EPS ? 1 : d > 0. ? 2 :
	                                     0;
}
int intersect(const line &l, const circle &c) { return intersect(c, l); }
int intersect(const circle &c, const point &p) { return int(eq(c.radius, distance(c.center, p))); }
int intersect(const point &p, const circle &c) { return intersect(c, p); }
int intersect(const segment &s, const segment &t) {
	if(same_point(s.a, s.b)) return intersect(t, s.a);
	if(intersect(line(s), t.a) && intersect(line(s), t.b) && std::max(std::min(s.a, s.b), std::min(t.a, t.b)) < std::min(std::max(s.a, s.b), std::max(t.a, t.b)))
		return -1;
	return int(ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0);
}
int intersect(const circle &c, const segment &s) {
	const point h = projection(s, c.center);
	const int c0 = compare(distance(h, c.center), c.radius);
	if(c0 == 1) return 0;
	if(c0 == 0) return intersect(s, h);
	const int c1 = compare(distance(c.center, s.a), c.radius), c2 = compare(distance(c.center, s.b), c.radius);
	if(std::min(c1, c2) == -1) return int(std::max(c1, c2) >= 0);
	return intersect(s, h) ? 2 : 0;
}
int intersect(const segment &s, const circle &c) { return intersect(c, s); }
int intersect(const circle &c1, const circle &c2) { return 2 - abs(2 - number_of_common_tangents(c1, c2)); }

// distance of two shaps
R distance(const point &a, const point &b) { return fabs(a - b); }
R distance(const line &l, const point &p) { return distance(p, projection(l, p)); }
R distance(const point &p, const line &l) { return distance(l, p); }
R distance(const line &l, const line &m) { return parallel(l, m) ? distance(l, m.a) : 0; }
R distance(const segment &s, const point &p) {
	const point r = projection(s, p);
	return intersect(s, r) ? distance(r, p) : std::min(distance(s.a, p), distance(s.b, p));
}
R distance(const point &p, const segment &s) { return distance(s, p); }
R distance(const segment &a, const segment &b) {
	if(intersect(a, b)) return R(0);
	return std::min({distance(a, b.a), distance(a, b.b), distance(b, a.a), distance(b, a.b)});
}
R distance(const line &l, const segment &s) {
	if(intersect(l, s)) return 0;
	return std::min(distance(l, s.a), distance(l, s.b));
}
R distance(const segment &s, const line &l) { return distance(l, s); }
R distance(const circle &c, const point &p) { return fabsl(distance(c.center, p) - c.radius); }
R distance(const point &p, const circle &c) { return distance(c, p); }
R distance(const circle &c, const line &l) { return std::max(R(0), distance(l, c.center) - c.radius); }
R distance(const line &l, const circle &c) { return distance(c, l); }
R distance(const circle &c1, const circle &c2) {
	const R d = distance(c1.center, c2.center);
	if(d > c1.radius + c2.radius) return d - c1.radius - c2.radius;
	if(d < fabsl(c1.radius - c2.radius)) return fabsl(c1.radius - c2.radius) - d;
	return R(0);
}
R distance(const circle &c, const segment &s) {
	const point p = projection(s, c.center);
	const R dist_min = intersect(s, p) ? distance(c.center, p) : std::min(distance(c.center, s.a), distance(c.center, s.b));
	if(dist_min > c.radius) return dist_min - c.radius;
	const R dist_max = std::max(distance(c.center, s.a), distance(c.center, s.b));
	return dist_max < c.radius ? c.radius - dist_max : R(0);
}
R distance(const segment &s, const circle &c) { return distance(c, s); }

point crosspoint(const line &l, const line &m) {
	R A = cross(l.b - l.a, m.b - m.a);
	R B = cross(l.b - l.a, l.b - m.a);
	if(eq(A, 0.)) return m.a;
	return m.a + (m.b - m.a) * B / A;
}
point crosspoint(const segment &s, const segment &t) { return crosspoint(line(s), line(t)); }
point crosspoint(const segment &s, const line &l) { return crosspoint(line(s), l); }
point crosspoint(const line &l, const segment &s) { return crosspoint(l, line(s)); }
points crosspoints(const circle &c, const line &l) {
	const point pr = projection(l, c.center);
	const R square = c.radius * c.radius - norm(pr - c.center);
	switch(sgn(square)) {
		case 0 :
			return points{pr};
		case -1 :
			return points(0);
	}
	const arrow v = (l.b - l.a) / abs(l.b - l.a) * sqrtl(square);
	return points{pr - v, pr + v};
}
points crosspoints(const line &l, const circle &c) { return crosspoints(c, l); }
points crosspoints(const circle &c, const segment &s) {
	points ret;
	for(const auto &pt : crosspoints(c, line(s)))
		if(intersect(s, pt)) ret.push_back(pt);
	return ret;
}
points crosspoints(const segment &s, const circle &c) { return crosspoints(c, s); }
points crosspoints(const circle &c1, const circle &c2) {
	R d = abs(c1.center - c2.center);
	if(compare(d, c1.radius + c2.radius) == 1) return points(0);
	if(compare(d, fabsl(c1.radius - c2.radius)) == -1) return points(0);
	bool one_crosspoint = false;
	if(eq(d, c1.radius + c2.radius) || eq(d, fabsl(c1.radius - c2.radius))) one_crosspoint = true;
	const R alpha = acosl((c1.radius * c1.radius + d * d - c2.radius * c2.radius) / (2 * c1.radius * d));  // cosine theorem
	const R beta = std::arg(c2.center - c1.center);
	if(one_crosspoint) return points{c1.center + std::polar(c1.radius, beta + alpha)};
	return points{c1.center + std::polar(c1.radius, beta + alpha), c1.center + std::polar(c1.radius, beta - alpha)};
}

points tangent_points(const circle &c, const point &p) {
	const R square = norm(c.center - p) - c.radius * c.radius;
	switch(sgn(square)) {
		case 0 :
			return points{p};
		case -1 :
			return points{};
	}
	return crosspoints(c, circle(p, sqrtl(square)));
}

// common tangents of two circles
lines tangents(circle c1, circle c2) {
	lines ret;
	if(c1.radius < c2.radius) std::swap(c1, c2);
	const R g = distance(c1.center, c2.center);
	if(!sgn(g)) return ret;
	const arrow u = (c2.center - c1.center) / g;
	const arrow v = rotate(u, PI * 0.5);
	for(const int &s : {-1, 1}) {
		const R h = (c1.radius + s * c2.radius) / g;
		if(eq(1 - h * h, 0)) {
			ret.emplace_back(c1.center + u * c1.radius, c1.center + (u + v) * c1.radius);
		} else if(1 - h * h > 0) {
			const point uu = u * h, vv = v * sqrtl(1 - h * h);
			ret.emplace_back(c1.center + (uu + vv) * c1.radius, c2.center - (uu + vv) * c2.radius * R(s));
			ret.emplace_back(c1.center + (uu - vv) * c1.radius, c2.center - (uu - vv) * c2.radius * R(s));
		}
	}
	return ret;
}


enum CONTAIN { OUT = 0,
	           ON = 1,
	           IN = 2 };
int contains(const polygon &poly, const point &p) {
	bool in = false;
	for(int i = 0; i < poly.size(); i++) {
		point a = poly[i], b = poly[(i + 1) % poly.size()];
		if(ccw(a, b, p) == 0) return CONTAIN::ON;
		if(a.imag() > b.imag()) swap(a, b);
		if(a.imag() <= p.imag() && p.imag() < b.imag() && cross(a - p, b - p) < 0) in = !in;
	}
	return in ? CONTAIN::IN : CONTAIN::OUT;
}
int contains(const circle &c, const point &p) { return compare(c.radius, distance(c.center, p)) + 1; }

bool is_convex(const polygon &p, bool pi_is_ok = true) {
	int n = (int)p.size();
	if(pi_is_ok) {
		for(int i = 0; i < n; i++)
			if(ccw(p[i], p[(i + 1) % n], p[(i + 2) % n]) == -1) return false;
	} else {
		for(int i = 0; i < n; i++)
			if(ccw(p[i], p[(i + 1) % n], p[(i + 2) % n]) != 1) return false;
	}
	return true;
}

polygon convex_hull(polygon &p, bool vertices_on_edge_remain = true) {
	int n = (int)p.size(), k = 0;
	if(n <= 2) return p;
	sort(p.begin(), p.end());
	points ch(2 * n);
	if(vertices_on_edge_remain) {
		for(int i = 0; i < n; ch[k++] = p[i++])
			while(k >= 2 && ccw(ch[k - 2], ch[k - 1], p[i]) == -1) --k;
		for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--])
			while(k >= t && ccw(ch[k - 2], ch[k - 1], p[i]) == -1) --k;
	} else {
		for(int i = 0; i < n; ch[k++] = p[i++])
			while(k >= 2 && ccw(ch[k - 2], ch[k - 1], p[i]) != 1) --k;
		for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--])
			while(k >= t && ccw(ch[k - 2], ch[k - 1], p[i]) != 1) --k;
	}
	ch.resize(k - 1);
	return ch;
}

// cut the convex polygon 'U' with line 'a'-'b', then return the leftside polygon
// (i.e. forall p \in (returned polygon), ccw(a, b, p) != -1)
// only 0~2 points may be returned
polygon convex_cut(const polygon &U, const point &a, const point &b) {
	polygon ret;
	const line l(a, b);
	for(int i = 0; i < U.size(); i++) {
		const point &now = U[i], &nxt = U[(i + 1) % U.size()];
		if(ccw(l.a, l.b, now) != -1) ret.push_back(now);
		if(ccw(l.a, l.b, now) * ccw(l.a, l.b, nxt) == -1) ret.push_back(crosspoint(line(now, nxt), l));
	}
	return ret;
}


void main_();
int main() {
	int t = 1;
	while(t--) main_();
}

void main_() {
	INT(n, k);
	points rp, bp;
	rep(i, n) {
		INT(x, y, c);
		if(c == 1)
			rp.push_back(point{x, y});
		else
			bp.push_back(point{x, y});
	}
	if(rp.empty() or bp.empty()) {
		No();
		return;
	}
	if(k >= 4) {
		auto rh = convex_hull(rp);
		auto bh = convex_hull(bp);
		bool res = 0;
		foa(v, rh) {
			if(contains(bh, v)) res = 1;
		}
		foa(v, bh) {
			if(contains(rh, v)) res = 1;
		}
		rep(i, SZ(rh)) {
			rep(j, SZ(bh)) {
				auto l1 = segment(rh[i], rh[(i + 1) % SZ(rh)]);
				auto l2 = segment(bh[i], bh[(i + 1) % SZ(bh)]);
				if(intersect(l1, l2)) res = 1;
			}
		}
		Yes(res);
	} else {
		rep(_, 2) {
			for(auto b : bp) {
				set<pii> st;
				for(auto r : rp) {
					int dx = r.real() - b.real();
					int dy = r.imag() - b.imag();
					int g = gcd(dx, dy);
					dx /= g, dy /= g;
					if(st.count({-dx, -dy})) {
						Yes();
						return;
					}
					st.insert({dx, dy});
				}
			}
			swap(rp, bp);
		}
		No();
	}
}