#define _USE_MATH_DEFINES
#define _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"
#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 = (int)1e9;
constexpr ll inf_ll = (ll)1e18, MOD = 1000000007;
constexpr ld PI = M_PI, EPS = 1e-12;

// --- input --- //
#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);
	}
	struct InputV {
		int n, id;
		InputV(int _n) :n(_n), id(0) {}
		InputV(const pair<int, int>& nm) :n(nm.first), id(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>(id)); i(v); return v;
		}
	};
public:
	static string get_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)...);
	}
#define input(T) Input::in<T>()
#define INT input(int)
#define LL input(ll)
#define STR input(string)
#define inputs(T, ...) T __VA_ARGS__; in(__VA_ARGS__)
#define ini(...) inputs(int, __VA_ARGS__)
#define inl(...) inputs(ll, __VA_ARGS__)
#define ins(...) inputs(string, __VA_ARGS__)
}in;

// --- output --- //
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 {
		if (v < 0)putchar_unlocked('-'), v = -v;
		char b[10]; int i = 0;
		while (v)b[i++] = '0' + v % 10, v /= 10;
		if (!i)b[i++] = '0';
		while (i--)putchar_unlocked(b[i]);
	}
	void p(ll v)const {
		if (v < 0)putchar_unlocked('-'), v = -v;
		char b[20]; int i = 0;
		while (v)b[i++] = '0' + v % 10, v /= 10;
		if (!i)b[i++] = '0';
		while (i--)putchar_unlocked(b[i]);
	}
	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(ld 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;

// --- step --- //
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 count()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 count()const {
		return be.count();
	}
	constexpr T step()const {
		return be.step();
	}
	constexpr T sum()const {
		return start() * count() + step() * (count() * (count() - 1) / 2);
	}
	operator vector<T>()const {
		return as_vector();
	}
	template<class F>void each(const F& f)const {
		for (T i : *this)f(i);
	}
	auto as_vector()const {
		vector<T> res; res.reserve(count()); each([&](T i) {res.push_back(i); }); return res;
	}
	template<class F, class U = decay_t<result_of_t<F(T)>>>auto map(const F& f)const {
		vector<U> res; res.reserve(count()); each([&](T i) {res.push_back(f(i)); }); return res;
	}
	template<class F>auto select(const F& f)const {
		vector<T> res; each([&](T i) {if (f(i))res.push_back(i); }); return res;
	}
	template<class F>int count_if(const F& f)const {
		int res = 0; each([&](T i) {if (f(i))++res; }); return res;
	}
	template<class F>T find_if(const F& f)const {
		for (T i : *this)if (f(i))return i; return 0;
	}
	template<class F>auto max_by(const F& f)const {
		auto v = map(f); return *max_element(v.begin(), v.end());
	}
	template<class F>auto min_by(const F& f)const {
		auto v = map(f); return *min_element(v.begin(), v.end());
	}
	template<class F>bool all_of(const F& f)const {
		for (T i : *this)if (!f(i))return false; return true;
	}
	template<class F>bool any_of(const F& f)const {
		for (T i : *this)if (f(i))return true; return false;
	}
	template<class F, class U = decay_t<result_of_t<F(T)>>>auto sum(const F& f)const {
		U res = 0; each([&](T i) {res += static_cast<U>(f(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);
}

// --- functions --- //
inline namespace {
	template<class T>inline void Sort(T& a) {
		sort(all(a));
	}
	template<class T>inline void RSort(T& a) {
		sort(rall(a));
	}
	template<class T, class F>inline void Sort(T& a, const F& f) {
		sort(all(a), f);
	}
	template<class T, class F>inline void RSort(T& a, const F& f) {
		sort(rall(a), f);
	}
	template<class T>inline T Sorted(T a) {
		Sort(a); return a;
	}
	template<class T>inline T RSorted(T a) {
		RSort(a); return a;
	}
	template<class T, class F>inline T Sorted(T& a, const F& f) {
		Sort(a, f); return a;
	}
	template<class T, class F>inline T RSorted(T& a, const F& f) {
		RSort(a, f); return a;
	}
	template<class T, class F>inline void SortBy(T& a, const F& f) {
		sort(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class F>inline void RSortBy(T& a, const F& f) {
		sort(rall(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T>inline void Reverse(T& a) {
		reverse(all(a));
	}
	template<class T>inline void Unique(T& a) {
		a.erase(unique(all(a)), a.end());
	}
	template<class T>inline void Uniq(T& a) {
		Sort(a); Unique(a);
	}
	template<class T>inline void Rotate(T& a, int left) {
		rotate(a.begin(), a.begin() + left, a.end());
	}
	template<class T>inline T Reversed(T a) {
		Reverse(a); return a;
	}
	template<class T>inline T Uniqued(T a) {
		Unique(a); return a;
	}
	template<class T>inline T Uniqed(T a) {
		Uniq(a); return a;
	}
	template<class T>inline T Rotated(T a, int left) {
		Rotate(a, left); return a;
	}
	template<class T>inline auto Max(const T& a) {
		return *max_element(all(a));
	}
	template<class T>inline auto Min(const T& a) {
		return *min_element(all(a));
	}
	template<class T>inline int MaxPos(const T& a) {
		return max_element(all(a)) - a.begin();
	}
	template<class T>inline int MinPos(const T& a) {
		return min_element(all(a)) - a.begin();
	}
	template<class T, class F>inline auto MaxBy(const T& a, const F& f) {
		return *max_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class F>inline auto MinBy(const T& a, const F& f) {
		return *min_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class U>inline int Count(const T& a, const U& v) {
		return count(all(a), v);
	}
	template<class T, class F>inline int CountIf(const T& a, const F& f) {
		return count_if(all(a), f);
	}
	template<class T, class U>inline int Find(const T& a, const U& v) {
		return find(all(a), v) - a.begin();
	}
	template<class T, class F>inline int FindIf(const T& a, const F& f) {
		return find_if(all(a), f) - a.begin();
	}
	template<class T, class U = typename T::value_type>inline U Sum(const T& a) {
		return accumulate(all(a), U());
	}
	template<class T, class U>inline bool Includes(const T& a, const U& v) {
		return find(all(a), v) != a.end();
	}
	template<class T, class F>inline auto Sum(const T& v, const F& f) {
		return accumulate(next(v.begin()), v.end(), f(*v.begin()), [&](auto a, auto b) {return a + f(b); });
	}
	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, class F>inline void RemoveIf(T& a, const F& f) {
		a.erase(remove_if(all(a), f), a.end());
	}
	template<class F>inline auto Vector(size_t size, const F& f) {
		vector<decay_t<result_of_t<F(size_t)>>> res(size);
		for (size_t i = 0; i < size; ++i)res[i] = f(i);
		return res;
	}
	template<class T>inline auto Grid(size_t h, size_t w, const T& v = T()) {
		return vector<vector<T>>(h, vector<T>(w, v));
	}
	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, class F>inline auto Each(T& v, F&& f) {
		for (auto& i : v)f(i);
	}
	template<class T, class F>inline auto Each(const T& v, F&& f) {
		for (const auto& i : v)f(i);
	}
	template<class T, class F>inline auto Select(const T& v, const F& f) {
		T res;
		for (const auto& e : v)if (f(e))res.push_back(e);
		return res;
	}
	template<class T, class F>inline auto Map(const T& v, F&& f) {
		vector<decay_t<result_of_t<F(typename T::value_type)>>> res(v.size());
		size_t i = 0; for (const auto& e : v)res[i++] = f(e);
		return res;
	}
	template<class T, class F>inline auto MapIndex(const T& v, const F& f) {
		vector<decay_t<result_of_t<F(size_t, typename T::value_type)>>> res(v.size());
		size_t i = 0; for (auto it = v.begin(); it != v.end(); ++it, ++i)res[i] = f(i, *it);
		return res;
	}
	template<class T, class F>inline auto TrueIndex(const T& v, const F& f) {
		vector<size_t> res;
		for (size_t i = 0; i < v.size(); ++i)if (f(v[i]))res.push_back(i);
		return res;
	}
	template<class T, class U = typename T::value_type>inline auto Indexed(const T& v) {
		vector<pair<U, int>> res(v.size());
		for (int i = 0; i < (int)v.size(); ++i)res[i] = make_pair(static_cast<U>(v[i]), i);
		return res;
	}
	inline auto operator*(string s, size_t n) {
		string res;
		for (size_t i = 0; i < n; ++i)res += s;
		return res;
	}
	template<class T>inline auto& operator<<(vector<T>& v, const vector<T>& v2) {
		v.insert(v.end(), all(v2)); return v;
	}
	template<class T>inline T Ceil(T n, T id) {
		return (n + id - 1) / id;
	}
	template<class T>inline T Ceil2(T n, T id) {
		return Ceil(n, id) * id;
	}
	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;
	}
	inline int pop_count(int n) {
		return bitset<32>(n).count();
	}
	inline int pop_count(ll n) {
		return bitset<64>(n).count();
	}
	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 = ll>inline T BIT(int b) {
		return T(1) << b;
	}
	template<class T>inline T Gcd(T n, T id) {
		return id ? Gcd(id, n % id) : n;
	}
	template<class T>inline T Lcm(T n, T id) {
		return n / Gcd(n, id) * id;
	}
	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>);
	}
	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>);
	}
	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 id = MOD) {
		T r = 1; while (n > 0) { if (n & 1)r = r * a % id, n--; else a = a * a % id, n /= 2; }return r;
	}
}

// --- dump --- //
#if __has_include("dump.hpp")
#include "dump.hpp"
#else
#define dump(...) ((void)0)
#endif

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

constexpr bool Equal(ld a, ld b) { return a < b ? b - a < EPS : a - b < EPS; }
struct Vec2 {
	ld x, y;
	constexpr Vec2() :x(0), y(0) {}
	constexpr Vec2(ld _x, ld _y) : x(_x), y(_y) {}
	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); }
	ld dist(const Vec2& v)const { return hypot(x - v.x, y - v.y); }
	Vec2 abs(const Vec2& v)const { return { std::abs(x - v.x),std::abs(y - v.y) }; }
	Vec2& swap() { std::swap(x, y); return *this; }
	constexpr ld sqr_norm()const { return x * x + y * y; }
	ld norm()const { return sqrt(sqr_norm()); }
	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; }
};

int main() {
	int n = in;
	vector<Vec2> p(n), d(n);
	vector<char> ch(n);
	rep(i, n) {
		in(p[i], ch[i]);
		if (ch[i] == 'R') {
			d[i] = Vec2(1, 0);
		} else if (ch[i] == 'L') {
			d[i] = Vec2(-1, 0);
		} else if (ch[i] == 'U') {
			d[i] = Vec2(0, 1);
		} else if (ch[i] == 'D') {
			d[i] = Vec2(0, -1);
		}
	}

	auto calc_area = [&](ld time) {
		Vec2 mi(inf, inf), ma(-inf, -inf);
		rep(i, n) {
			Vec2 v = p[i] + d[i] * time;
			chmin(mi.x, v.x);
			chmin(mi.y, v.y);
			chmax(ma.x, v.x);
			chmax(ma.y, v.y);
		}
		return (ma.x - mi.x) * (ma.y - mi.y);
	};

	VD ivent{ 0,1 };
	{ // x_max
		ld left = -inf, right = -inf, no = -inf;
		rep(i, n) {
			if (ch[i] == 'L') {
				chmax(left, p[i].x);
			} else if (ch[i] == 'R') {
				chmax(right, p[i].x);
			} else {
				chmax(no, p[i].x);
			}
		}
		if (left > -inf && right > -inf)ivent.push_back((left - right) / 2.0);
		if (right > -inf && no > -inf)  ivent.push_back(no - right);
		if (left > -inf && no > -inf)   ivent.push_back(left - no);
	}
	{ // x_min
		ld left = inf, right = inf, no = inf;
		rep(i, n) {
			if (ch[i] == 'L') {
				chmin(left, p[i].x);
			} else if (ch[i] == 'R') {
				chmin(right, p[i].x);
			} else {
				chmin(no, p[i].x);
			}
		}
		if (left < inf && right < inf)ivent.push_back((left - right) / 2.0);
		if (right < inf && no < inf)  ivent.push_back(no - right);
		if (left < inf && no < inf)   ivent.push_back(left - no);
	}
	{ // y_max
		ld down = -inf, up = -inf, no = -inf;
		rep(i, n) {
			if (ch[i] == 'D') {
				chmax(down, p[i].y);
			} else if (ch[i] == 'U') {
				chmax(up, p[i].y);
			} else {
				chmax(no, p[i].y);
			}
		}
		if (down > -inf && up > -inf)ivent.push_back((down - up) / 2.0);
		if (up > -inf && no > -inf)  ivent.push_back(no - up);
		if (down > -inf && no > -inf)ivent.push_back(down - no);
	}
	{ // y_min
		ld down = inf, up = inf, no = inf;
		rep(i, n) {
			if (ch[i] == 'D') {
				chmin(down, p[i].y);
			} else if (ch[i] == 'U') {
				chmin(up, p[i].y);
			} else {
				chmin(no, p[i].y);
			}
		}
		if (down < inf && up < inf)ivent.push_back((down - up) / 2.0);
		if (up < inf && no < inf)  ivent.push_back(no - up);
		if (down < inf && no < inf)ivent.push_back(down - no);
	}

	Sort(ivent);
	ld ans = inf_ll;
	for (ld t : ivent) {
		chmin(ans, calc_area(abs(t)));
	}
	out(ans);
}

/*

5
-7 -10 U
7 -6 U
-8 7 D
-3 3 D
0 -6 R

6.5
-7 -3.5
7 0.5
-8 0.5
-3 -3.5
6.5 -6


*/

Measured memory_bytes: 6656