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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
	
	static final int MAX = 400000000;
	
	public static void main(String[] args) throws IOException {
		MyScanner sc = new MyScanner();
		PrintWriter out = new PrintWriter(System.out);
		int N = sc.nextInt();
		int l = 2 * MAX, l1 = 2 * MAX, l2 = 2 * MAX, r = -2 * MAX, r1 = -2 * MAX, r2 = -2 * MAX;
		int d = 2 * MAX, d1 = 2 * MAX, d2 = 2 * MAX, u = -2 * MAX, u1 = -2 * MAX, u2 = -2 * MAX;
		int x, y;
		char c;
		for (int i = 0; i < N; i++) {
			x = sc.nextInt() * 2;
			y = sc.nextInt() * 2;
			c = sc.next().charAt(0);
			if (c == 'L') {
				l2 = Math.min(l2, x);
				r2 = Math.max(r2, x);
			} else if (c == 'R') {
				l1 = Math.min(l1, x);
				r1 = Math.max(r1, x);
			} else {
				l = Math.min(l, x);
				r = Math.max(r, x);
			}
			if (c == 'D') {
				d2 = Math.min(d2, y);
				u2 = Math.max(u2, y);
			} else if (c == 'U') {
				d1 = Math.min(d1, y);
				u1 = Math.max(u1, y);
			} else {
				d = Math.min(d, y);
				u = Math.max(u, y);
			}
		}
		long ans = MAX * (long)MAX, first, second;
		for (int t = 0; t <= MAX; t++) {
			first = Math.max(r, Math.max(r1, r2)) - Math.min(l, Math.min(l1, l2));
			second = Math.max(u, Math.max(u1, u2)) - Math.min(d, Math.min(d1, d2));
			ans = Math.min(ans, first * second);
			l1++; r1++; d1++; u1++;
			l2--; r2--; d2--; u2--;
		}
		out.println(ans / 4.0);
		
		out.flush();
	}
	
	static class MyScanner {
		private BufferedReader br;
		private StringTokenizer tokenizer;
		
		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
	}
}