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.*;
import java.io.*;
public class Main {

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		Coor[] cs = new Coor[n];
		for(int i = 0; i < n; i++){
			st = new StringTokenizer(br.readLine());
			int x = Integer.parseInt(st.nextToken());
			int y = Integer.parseInt(st.nextToken());
			char d = st.nextToken().charAt(0);
			cs[i] = new Coor(x, y, d);
		}
		double a = 0, b = 2*1e8+1;
		for(int iter = 0; iter < 200; iter++){
			double c = (2*a+b)/3;
			double d = (a+2*b)/3;
			double C = eval(cs, c);
			double D = eval(cs, d);
			if(C < D) b = d;
			else a = c;
		}
		System.out.println(eval(cs, a));
	}
	static double eval(Coor[] cs, double t){
		double maxx = -1e8, maxy = -1e8, minx = 1e8, miny = 1e8;
		for(Coor c: cs){
			double x = c.movex(t);
			double y = c.movey(t);
			maxx = Double.max(maxx, x);
			minx = Double.min(minx, x);
			miny = Double.min(miny, y);
			maxy = Double.max(maxy, y);
		}
		return (maxx - minx)*(maxy - miny);
	}
	static class Coor{
		int x, y; char d;
		public Coor(int x, int y, char d){
			this.x = x; this.y = y; this.d = d;
		}
		public String toString(){
			return x+" "+y;
		}
		public double movex(double t){
			if(d == 'L') return x-t;
			else if(d == 'R') return x+t;
			else return x;
		}
		public double movey(double t){
			if(d == 'U') return y+t;
			else if(d == 'D') return y-t;
			else return y;
		}
	}
	static class CoorNS implements Comparable<CoorNS>{
		int x, y; char d;
		public CoorNS(int x, int y, char d){
			this.x = x; this.y = y; this.d = d;
		}
		@Override
		public int compareTo(CoorNS c) {
			return y - c.y;
		}
		public String toString(){
			return x+" "+y;
		}
	}
	static class CoorWE implements Comparable<CoorWE>{
		int x, y; char d;
		public CoorWE(int x, int y, char d){
			this.x = x; this.y = y; this.d = d;
		}
		@Override
		public int compareTo(CoorWE c) {
			return x - c.x;
		}
		public String toString(){
			return x+" "+y;
		}
	}

}