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 Julia (0.5.0) (judge verdict: Accepted)

function main()
	lines=readlines();
	N=parse(Int,shift!(lines))
	INF=10^9
	mx=[INF,INF,INF,INF]
	my=mx[:]
	Mx=-mx
	My=Mx[:]
	for i=1:N
		x,y,d=split(shift!(lines))
		x=parse(Int,x)
		y=parse(Int,y)
		if d=="L"
			d=1
		elseif d=="R"
			d=2
		elseif d=="U"
			d=3
		elseif d=="D"
			d=4
		end
		mx[d]=min(mx[d],x)
		my[d]=min(my[d],y)
		Mx[d]=max(Mx[d],x)
		My[d]=max(My[d],y)
	end
	T=[0.0]
	push!(T,(mx[1]-mx[2])/2)
	push!(T,mx[1]-min(mx[3],mx[4]))
	push!(T,min(mx[3],mx[4])-mx[2])
	push!(T,(Mx[1]-Mx[2])/2)
	push!(T,Mx[1]-max(Mx[3],Mx[4]))
	push!(T,max(Mx[3],Mx[4])-Mx[2])
	push!(T,(my[4]-my[3])/2)
	push!(T,my[4]-min(my[1],my[2]))
	push!(T,min(my[1],my[2])-my[3])
	push!(T,(My[4]-My[3])/2)
	push!(T,My[4]-max(My[1],My[2]))
	push!(T,max(My[1],My[2])-My[3])
	ans=10^18
	for t=T
		if t<0;continue;end
		X=max(Mx[1]-t,Mx[2]+t,Mx[3],Mx[4])-min(mx[1]-t,mx[2]+t,mx[3],mx[4])
		Y=max(My[1],My[2],My[3]+t,My[4]-t)-min(my[1],my[2],my[3]+t,my[4]-t)
		ans=min(ans,X*Y)
	end
	println(ans)
end
main()