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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n = gets.to_i
point = Array.new(n).map{Array.new(3,"")}
n.times{|i| point[i] = gets.chomp.split}
#固定、離れる、近づく
xmin = [10**8,10**8,10**8]
xmax = [-10**8,-10**8,-10**8]
ymin = [10**8,10**8,10**8]
ymax = [-10**8,-10**8,-10**8]
for i in 0..n-1
  if point[i][2] == "R"
    xmin[2] = point[i][0].to_i if xmin[2] > point[i][0].to_i
    xmax[1] = point[i][0].to_i if xmax[1] < point[i][0].to_i
    ymin[0] = point[i][1].to_i if ymin[0] > point[i][1].to_i
    ymax[0] = point[i][1].to_i if ymax[0] < point[i][1].to_i
  elsif point[i][2] == "L"
    xmin[1] = point[i][0].to_i if xmin[1] > point[i][0].to_i
    xmax[2] = point[i][0].to_i if xmax[2] < point[i][0].to_i
    ymin[0] = point[i][1].to_i if ymin[0] > point[i][1].to_i
    ymax[0] = point[i][1].to_i if ymax[0] < point[i][1].to_i
  elsif point[i][2] == "U"
    xmin[0] = point[i][0].to_i if xmin[0] > point[i][0].to_i
    xmax[0] = point[i][0].to_i if xmax[0] < point[i][0].to_i
    ymin[2] = point[i][1].to_i if ymin[2] > point[i][1].to_i
    ymax[1] = point[i][1].to_i if ymax[1] < point[i][1].to_i
  elsif point[i][2] == "D"
    xmin[0] = point[i][0].to_i if xmin[0] > point[i][0].to_i
    xmax[0] = point[i][0].to_i if xmax[0] < point[i][0].to_i
    ymin[1] = point[i][1].to_i if ymin[1] > point[i][1].to_i
    ymax[2] = point[i][1].to_i if ymax[2] < point[i][1].to_i
  end
end
ans = 10**15
for i in 0..(10**6)
  xmin0 = xmin[0].to_f
  xmin0 = xmin[1] - i*0.5 if xmin0 > xmin[1] - i*0.5
  xmin0 = xmin[2] + i*0.5 if xmin0 > xmin[2] + i*0.5
  xmax0 = xmax[0].to_f
  xmax0 = xmax[1] + i*0.5 if xmax0 < xmax[1] + i*0.5
  xmax0 = xmax[2] - i*0.5 if xmax0 < xmax[2] - i*0.5
  ymin0 = ymin[0].to_f
  ymin0 = ymin[1] - i*0.5 if ymin0 > ymin[1] - i*0.5
  ymin0 = ymin[2] + i*0.5 if ymin0 > ymin[2] + i*0.5
  ymax0 = ymax[0].to_f
  ymax0 = ymax[1] + i*0.5 if ymax0 < ymax[1] + i*0.5
  ymax0 = ymax[2] - i*0.5 if ymax0 < ymax[2] - i*0.5
  ans = (xmax0 - xmin0)*(ymax0 - ymin0) if ans > (xmax0 - xmin0)*(ymax0 - ymin0)
end
puts ans