Problem: 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}.

Examples

Input

2
0 3 D
3 0 L


Output

0


Input

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


Output

97.5


Input

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


Output

273

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        int[] x = new int[N];
        int[] y = new int[N];
        char[] d = new char[N];
        for (int i = 0; i < N; ++i) {
            x[i] = sc.nextInt();
            y[i] = sc.nextInt();
            d[i] = sc.next().charAt(0);
        }

        System.out.println(solve(x, y, d));

        sc.close();
    }

    static double solve(int[] x, int[] y, char[] d) {
        int xStillMin = Integer.MAX_VALUE;
        int xStillMax = Integer.MIN_VALUE;
        int xIncrMin = Integer.MAX_VALUE;
        int xIncrMax = Integer.MIN_VALUE;
        int xDecrMin = Integer.MAX_VALUE;
        int xDecrMax = Integer.MIN_VALUE;

        int yStillMin = Integer.MAX_VALUE;
        int yStillMax = Integer.MIN_VALUE;
        int yIncrMin = Integer.MAX_VALUE;
        int yIncrMax = Integer.MIN_VALUE;
        int yDecrMin = Integer.MAX_VALUE;
        int yDecrMax = Integer.MIN_VALUE;

        for (int i = 0; i < x.length; ++i) {
            x[i] *= 2;
            y[i] *= 2;

            if (d[i] == 'R') {
                xIncrMin = Math.min(xIncrMin, x[i]);
                xIncrMax = Math.max(xIncrMax, x[i]);

                yStillMin = Math.min(yStillMin, y[i]);
                yStillMax = Math.max(yStillMax, y[i]);
            } else if (d[i] == 'L') {
                xDecrMin = Math.min(xDecrMin, x[i]);
                xDecrMax = Math.max(xDecrMax, x[i]);

                yStillMin = Math.min(yStillMin, y[i]);
                yStillMax = Math.max(yStillMax, y[i]);
            } else if (d[i] == 'U') {
                xStillMin = Math.min(xStillMin, x[i]);
                xStillMax = Math.max(xStillMax, x[i]);

                yIncrMin = Math.min(yIncrMin, y[i]);
                yIncrMax = Math.max(yIncrMax, y[i]);
            } else {
                xStillMin = Math.min(xStillMin, x[i]);
                xStillMax = Math.max(xStillMax, x[i]);

                yDecrMin = Math.min(yDecrMin, y[i]);
                yDecrMax = Math.max(yDecrMax, y[i]);
            }
        }

        long minArea = Long.MAX_VALUE;
        int prevXDiff = Integer.MAX_VALUE;
        int prevYDiff = Integer.MAX_VALUE;
        while (true) {
            int xMin = Math.min(Math.min(xIncrMin, xDecrMin), xStillMin);
            int xMax = Math.max(Math.max(xIncrMax, xDecrMax), xStillMax);
            int xDiff = xMax - xMin;

            int yMin = Math.min(Math.min(yIncrMin, yDecrMin), yStillMin);
            int yMax = Math.max(Math.max(yIncrMax, yDecrMax), yStillMax);
            int yDiff = yMax - yMin;

            if (xDiff >= prevXDiff && yDiff >= prevYDiff) {
                break;
            }

            minArea = Math.min(minArea, (long) xDiff * yDiff);

            prevXDiff = xDiff;
            prevYDiff = yDiff;

            if (xIncrMin != Integer.MAX_VALUE) {
                ++xIncrMin;
                ++xIncrMax;
            }
            if (xDecrMin != Integer.MAX_VALUE) {
                --xDecrMin;
                --xDecrMax;
            }

            if (yIncrMin != Integer.MAX_VALUE) {
                ++yIncrMin;
                ++yIncrMax;
            }
            if (yDecrMin != Integer.MAX_VALUE) {
                --yDecrMin;
                --yDecrMax;
            }
        }

        return minArea / 4.0;
    }
}