output_description: 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}.
  
  * * *
input_description: 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
attempt: def analyze(points, left_static, right_static):
      """
      (x0, +1 or -1) in points
      """
  
      rightest_neg = -(10**9)
      leftest_neg = 10**9
      rightest_pos = -(10**9)
      leftest_pos = 10**9
      for x, d in points:
          if d == 1:
              rightest_pos = max(rightest_pos, x)
              leftest_pos = min(leftest_pos, x)
          else:
              rightest_neg = max(rightest_neg, x)
              leftest_neg = min(leftest_neg, x)
  
      max_t1 = rightest_neg - right_static
      max_t2 = right_static - rightest_pos
      if max_t1 > max_t2:
          max_t1 = max_t2 = (rightest_neg - rightest_pos) / 2
      max_t1 = max(0, max_t1)
      max_t2 = max(0, max_t2)
      max_x0 = max(rightest_pos, rightest_neg, right_static)
      max_x1 = max(rightest_pos + max_t1, rightest_neg - max_t1, right_static)
  
      def get_xmax(t):
          if t > max_t2:
              return max_x1 + t - max_t2
          elif t > max_t1:
              return max_x1
          else:
              return max_x0 - t
  
      min_t1 = left_static - leftest_pos
      min_t2 = leftest_neg - left_static
      if min_t1 > min_t2:
          min_t1 = min_t2 = (leftest_neg - leftest_pos) / 2
      min_t1 = max(0, min_t1)
      min_t2 = max(0, min_t2)
      min_x0 = min(leftest_pos, leftest_neg, left_static)
      min_x1 = min(leftest_pos + min_t1, leftest_neg - min_t1, left_static)
  
      def get_xmin(t):
          if t > min_t2:
              return min_x1 - t + min_t2
          elif t > min_t1:
              return min_x1
          else:
              return min_x0 + t
  
      T = sorted((max_t1, max_t2, min_t1, min_t2))
      D = [get_xmax(t) - get_xmin(t) for t in T]
      return T, D
  
  
  N = int(input())
  
  conv = {"R": 0, "U": 1, "L": 2, "D": 3}
  points = [
      (lambda i: (int(i[0]), int(i[1]), conv[i[2]]))(input().split()) for _ in range(N)
  ]
  
  
  xt, xd = analyze(
      [(x, 1 if d == 0 else -1) for x, y, d in points if d % 2 == 0],
      min((x for x, y, d in points if d % 2 == 1), default=10**9),
      max((x for x, y, d in points if d % 2 == 1), default=-(10**9)),
  )
  
  yt, yd = analyze(
      [(y, 1 if d == 1 else -1) for x, y, d in points if d % 2 == 1],
      min((y for x, y, d in points if d % 2 == 0), default=10**9),
      max((y for x, y, d in points if d % 2 == 0), default=-(10**9)),
  )
  
  
  def get_w(t):
      a, b, c, d = xt
  
      if t < a:
          return -2, xd[0] + 2 * a
      elif t < b:
          return -1, xd[0] + a
      elif t < c:
          return 0, xd[1]
      elif t < d:
          return 1, xd[2] - c
      else:
          return 2, xd[3] - 2 * d
  
  
  def get_h(t):
      a, b, c, d = yt
  
      if t < a:
          return -2, yd[0] + 2 * a
      elif t < b:
          return -1, yd[0] + a
      elif t < c:
          return 0, yd[1]
      elif t < d:
          return 1, yd[2] - c
      else:
          return 2, yd[3] - 2 * d
  
  
  T = sorted(xt + yt)
  
  
  def it():
      ne = iter(T)
      next(ne)
      for a, b in zip(T, ne):
          t = (a + b) / 2
  
          wa, wb = get_w(t)
          ha, hb = get_h(t)
          if wa * ha > 0 and a < -(wb * ha + wa * hb) / (2 * wa * ha) < b:
              t = -(wb * ha + wa * hb) / (2 * wa * ha)
              yield ((wa * t + wb) * (ha * t + hb), t)
          else:
              yield ((wa * a + wb) * (ha * a + hb), a)
              yield ((wa * b + wb) * (ha * b + hb), b)
  
  
  print(min(it())[0])
  
problem_description: 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.
samples: [{"input": "2\n    0 3 D\n    3 0 L", "output": "0\n    \n\nAfter three seconds, the two points will meet at the origin. The value in\nquestion will be 0 at that moment.\n\n* * *"}, {"input": "5\n    -7 -10 U\n    7 -6 U\n    -8 7 D\n    -3 3 D\n    0 -6 R", "output": "97.5\n    \n\nThe answer may not be an integer.\n\n* * *"}, {"input": "20\n    6 -10 R\n    -4 -9 U\n    9 6 D\n    -3 -2 R\n    0 7 D\n    4 5 D\n    10 -10 U\n    -1 -8 U\n    10 -6 D\n    8 -5 U\n    6 4 D\n    0 3 D\n    7 9 R\n    9 -4 R\n    3 10 D\n    1 9 U\n    1 -6 U\n    9 -8 R\n    6 7 D\n    7 -3 D", "output": "273"}]