Problem:
Score : 600 points

Problem Statement

There are N points in a two-dimensional plane. The initial coordinates of the i-th point are (x_i, y_i). Now, each point starts moving at a speed of 1 per second, in a direction parallel to the x- or y- axis. You are given a character d_i that represents the specific direction in which the i-th point moves, as follows:

If d_i = R, the i-th point moves in the positive x direction;

If d_i = L, the i-th point moves in the negative x direction;

If d_i = U, the i-th point moves in the positive y direction;

If d_i = D, the i-th point moves in the negative y direction.

You can stop all the points at some moment of your choice after they start moving (including the moment they start moving).
Then, let x_{max} and x_{min} be the maximum and minimum among the x-coordinates of the N points, respectively. Similarly, let y_{max} and y_{min} be the maximum and minimum among the y-coordinates of the N points, respectively.

Find the minimum possible value of (x_{max} - x_{min}) \times (y_{max} - y_{min}) and print it.

Constraints

1 \leq N \leq 10^5

-10^8 \leq x_i,\ y_i \leq 10^8

x_i and y_i are integers.

d_i is R, L, U, or D.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1 d_1
x_2 y_2 d_2
.
.
.
x_N y_N d_N

Output

Print the minimum possible value of (x_{max} - x_{min}) \times (y_{max} - y_{min}).

The output will be considered correct when its absolute or relative error from the judge's output is at most 10^{-9}.

Sample Input 1

2
0 3 D
3 0 L

Sample Output 1

0

After three seconds, the two points will meet at the origin. The value in question will be 0 at that moment.

Sample Input 2

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

Sample Output 2

97.5

The answer may not be an integer.

Sample Input 3

20
6 -10 R
-4 -9 U
9 6 D
-3 -2 R
0 7 D
4 5 D
10 -10 U
-1 -8 U
10 -6 D
8 -5 U
6 4 D
0 3 D
7 9 R
9 -4 R
3 10 D
1 9 U
1 -6 U
9 -8 R
6 7 D
7 -3 D

Sample Output 3

273

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#ifdef LOCAL111
	#define _GLIBCXX_DEBUG
#else
	#define NDEBUG
#endif
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
const int INF = 1e9;
using namespace std;
template<typename T, typename U> ostream& operator<< (ostream& os, const pair<T,U>& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; }

#define endl '\n'
#define ALL(a)  (a).begin(),(a).end()
#define SZ(a) int((a).size())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n)  FOR(i,0,n)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#ifdef LOCAL111
	#define DEBUG(x) cout<<#x<<": "<<(x)<<endl
	template<typename T> void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
#else
	#define DEBUG(x) true
	template<typename T> void dpite(T a, T b){ return; }
#endif
#define F first
#define S second
#define SNP string::npos
#define WRC(hoge) cout << "Case #" << (hoge)+1 << ": "
template<typename T> void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
template<typename T> bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;}
template<typename T> bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;}

typedef long long int LL;
typedef unsigned long long ULL;
typedef pair<int,int> P;

void ios_init(){
	cout.setf(ios::fixed);
	cout.precision(12);
#ifdef LOCAL111
	return;
#endif
	ios::sync_with_stdio(false); cin.tie(0);
}
const double EPS = 1e-20;

int main()
{
	ios_init();
	double w, h, x, y;
	while(cin >> w >> h >> x >> y) {
		auto f =[&](double x, double y) -> double {
			// if(y / x < h / w) {
				return h * w * y / x /2.;
			// } else {
			// 	return h * w * y / x /2.;
			// }
		};
		double ma = -1;
		int cnt = 0;
		REP(i, 2) REP(j, 2) {
			double nx = w - x;
			if(i) {
				nx = x;
			}
			double ny = h - y;
			if(j) {
				ny = y;
			}
			if(nx != 0) {
				double me = f(nx, ny);
				if(abs(ma - me) < EPS) {
					// cnt++;
				} else if(ma < me) {
					ma = me;
					// cnt = 0;
				}

			}
		}

		double me = min((h-y)*w, y * w);
		DEBUG(me);
		if(abs(ma - me) < EPS) {
			cnt++;
		} else if(ma < me) {
			ma = me;
			cnt = 0;
		}
		me = min((w-x)*h, x * h);
		DEBUG(me);
		if(abs(ma - me) < EPS) {
			cnt++;
		} else if(ma < me) {
			ma = me;
			cnt = 0;
		}
		DEBUG(cnt);

		cout << me << ' ' << int(cnt > 0) << endl;





		// double me = min((w-x) * h);
		// if(abs(mi - me) < EPS) {
		// 	cnt++;
		// } else if(mi > me) {
		// 	mi = f(h, w);
		// 	cnt = 0;
		// }
		
		// me = x * h;
		// if(abs(mi - f(h, w)) < EPS) {
		// 	cnt++;
		// } else if(mi > f(h, w)) {
		// 	mi = f(h, w);
		// 	cnt = 0;
		// }

		// if(abs(mi - f(h, w)) < EPS) {
		// 	cnt++;
		// } else if(mi > f(h, w)) {
		// 	mi = f(h, w);
		// 	cnt = 0;
		// }

		// if(abs(mi - f(h, w)) < EPS) {
		// 	cnt++;
		// } else if(mi > f(h, w)) {
		// 	mi = f(h, w);
		// 	cnt = 0;
		// }

	}
	return 0;
}