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())
M = {'R': [], 'L':[], 'U': [], 'D': [], 'X': [], 'Y': []}
for _ in range(N):
  x, y, d = input().split()
  if d in ['R', 'L']:
    M[d].append(int(x))
    M['Y'].append(int(y))
  else:
    M['X'].append(int(x))
    M[d].append(int(y))
for d in 'RLDUXY':
  M[d] = sorted(M[d])
T = [0] * 13
T[0] = M['X'][0] - M['R'][0] if M['X'] and M['R'] else -1
T[1] = M['L'][0] - M['X'][0] if M['X'] and M['L'] else -1
T[2] = (M['L'][0] - M['R'][0]) / 2 if M['L'] and M['R'] else -1
T[3] = M['X'][-1] - M['R'][-1] if M['X'] and M['R'] else -1
T[4] = M['L'][-1] - M['X'][-1] if M['X'] and M['L'] else -1
T[5] = (M['L'][-1] - M['R'][-1]) / 2 if M['L'] and M['R'] else -1
T[6] = M['Y'][-1] - M['U'][-1] if M['Y'] and M['U'] else -1
T[7] = M['D'][-1] - M['Y'][-1] if M['Y'] and M['D'] else -1
T[8] = (M['D'][-1] - M['U'][-1]) / 2 if M['D'] and M['U'] else -1
T[9] = M['Y'][0] - M['U'][0] if M['Y'] and M['U'] else -1
T[10] = M['D'][0] - M['Y'][0] if M['Y'] and M['D'] else -1
T[11] = (M['D'][0] - M['U'][0]) / 2 if M['D'] and M['U'] else -1
Rect = [-1] * 13
for i, t in enumerate(T):
  if t < 0:
    continue
  R = []
  L = []
  U = []
  D = []
  if M['R']:
    R.append(M['R'][-1] + t)
    L.append(M['R'][0] + t)
  if M['L']:
    R.append(M['L'][-1] - t)
    L.append(M['L'][0] - t)
  if M['U']:
    U.append(M['U'][-1] + t)
    D.append(M['U'][0] + t)
  if M['D']:
    U.append(M['D'][-1] - t)
    D.append(M['D'][0] - t)
  if M['X']:
    R.append(M['X'][-1])
    L.append(M['X'][0])
  if M['Y']:
    U.append(M['Y'][-1])
    D.append(M['Y'][0])
  Rect[i] = (max(R) - min(L)) * (max(U) - min(D))
print(min([r for r in Rect if r >= 0]))