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: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        F solver = new F();
        solver.solve(1, in, out);
        out.close();
    }

    static class F {
        long[] Rs = new long[]{-100000000000L, 100000000000L};
        long[] Ls = new long[]{-100000000000L, 100000000000L};
        long[] Us = new long[]{-100000000000L, 100000000000L};
        long[] Ds = new long[]{-100000000000L, 100000000000L};
        long[] xm = new long[]{-100000000000L, 100000000000L};
        long[] ym = new long[]{-100000000000L, 100000000000L};

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int N = in.nextInt();

            for (int i = 0; i < N; i++) {
                long x = in.nextLong();
                long y = in.nextLong();
                String d = in.next();
                switch (d) {
                    case "R":
                        Rs[0] = Math.max(Rs[0], x);
                        Rs[1] = Math.min(Rs[1], x);
                        ym[0] = Math.max(ym[0], y);
                        ym[1] = Math.min(ym[1], y);
                        break;
                    case "L":
                        Ls[0] = Math.max(Ls[0], x);
                        Ls[1] = Math.min(Ls[1], x);
                        ym[0] = Math.max(ym[0], y);
                        ym[1] = Math.min(ym[1], y);
                        break;
                    case "U":
                        xm[0] = Math.max(xm[0], x);
                        xm[1] = Math.min(xm[1], x);
                        Us[0] = Math.max(Us[0], y);
                        Us[1] = Math.min(Us[1], y);
                        break;
                    case "D":
                        xm[0] = Math.max(xm[0], x);
                        xm[1] = Math.min(xm[1], x);
                        Ds[0] = Math.max(Ds[0], y);
                        Ds[1] = Math.min(Ds[1], y);
                        break;
                }
            }

            double low = 0, hi = 1e8;
            while (true) {
                double temp1 = calc(low);
                double temp2 = calc(hi);
                if (Math.abs(temp1 - temp2) < 0.00000000001) {
                    break;
                }
                if (temp1 < temp2) {
                    hi -= (hi - low) / 3;
                } else {
                    low += (hi - low) / 3;
                }
            }
            out.printf("%.9f", calc(low));
        }

        private double calc(double diff) {
            double xmax = Math.max(xm[0], Math.max(Rs[0] + diff, Ls[0] - diff));
            double xmin = Math.min(xm[1], Math.min(Rs[1] + diff, Ls[1] - diff));
            double ymax = Math.max(ym[0], Math.max(Us[0] + diff, Ds[0] - diff));
            double ymin = Math.min(ym[1], Math.min(Us[1] + diff, Ds[1] - diff));
            return (xmax - xmin) * (ymax - ymin);
        }

    }
}