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 PYTHON3):

Solution:
N = int(input())
xyd = [list(input().split()) for _ in range(N)]

def nasu(s, e, f, n, inf):
  L = [0] * 3
  a, b, c = inf, inf, inf
  for i in range(N):
    t = int(xyd[i][n])
    if xyd[i][2] == s:
      a = f(a, t)
    elif xyd[i][2] == e:
      b = f(b, t)
    else:
      c = f(c, t)
  L[0] = a
  if f(a, c) == a:
    L[1] = abs(a - c)
  else:
    L[0], L[1] = c, 0
  if f(L[0], b) != b:
    if f(c, b) == c:
      L[2] = abs(b - c)
      if L[1] > L[2]:
        L[2] = abs(a - b) / 2
        L[1] = L[2]
    else:
      L[2] = abs(a - b) / 2
      L[1] = L[2]
  else:
    L = [b, 0, 0]
  for i in range(3):
    if abs(L[i]) > abs(inf) / 2:
      L[i] = abs(inf)
  return L

inf = 10 ** 10
R = nasu("L", "R", max, 0, -inf)
L = nasu("R", "L", min, 0, inf)
U = nasu("D", "U", max, 1, -inf)
D = nasu("U", "D", min, 1, inf)

def honya(x):
  r = honyaraka(R, x, 1)
  l = honyaraka(L, x, -1)
  u = honyaraka(U, x, 1)
  d = honyaraka(D, x, -1)
  return abs(r - l) * abs(u - d)

def honyaraka(X, x, f):
  a, b, c = X
  if x <= b:
    return a + x * f * -1
  if x < c:
    return a + b * f * -1
  return a + b * f * -1 + (x - c) * f

ans = honya(0)
T = [R, L, U, D]
for i in range(4):
  for j in range(1, 3):
    x = T[i][j]
    if x != inf:
      ans = min(ans, honya(x))

print(ans)