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())
out_of_range = 1000000000
r = [out_of_range+1, -out_of_range-1]
l = [out_of_range+1, -out_of_range-1]
u = [out_of_range+1, -out_of_range-1]
d = [out_of_range+1, -out_of_range-1]

x_fixed = [out_of_range+1, -out_of_range-1]
y_fixed = [out_of_range+1, -out_of_range-1]

for _ in range(n):
    x, y, di = input().split()
    x, y = int(x), int(y)
    if di == 'R':
        r[0], r[1] = min(x, r[0]), max(x, r[1])
        y_fixed[0] = min(y_fixed[0], y)
        y_fixed[1] = max(y_fixed[1], y)
    elif di == 'L':
        l[0], l[1] = min(x, l[0]), max(x, l[1])
        y_fixed[0] = min(y_fixed[0], y)
        y_fixed[1] = max(y_fixed[1], y)
    elif di == 'U':
        u[0], u[1] = min(y, u[0]), max(y, u[1])
        x_fixed[0] = min(x_fixed[0], x)
        x_fixed[1] = max(x_fixed[1], x)
    else:
        d[0], d[1] = min(y, d[0]), max(y, d[1])
        x_fixed[0] = min(x_fixed[0], x)
        x_fixed[1] = max(x_fixed[1], x)

exists_l = l[0] <= out_of_range
exists_r = r[0] <= out_of_range
exists_u = u[0] <= out_of_range
exists_d = d[0] <= out_of_range
exists_x_fixed = x_fixed[0] <= out_of_range
exists_y_fixed = y_fixed[0] <= out_of_range

def append_cross_time(l, r, time:set, contains_fixed:bool):
    for i in range(2):
        t = (l[i] - r[i])
        if t >= 0 :
            time.add(t if contains_fixed else t / 2)

time = {0}
if exists_l and exists_r:
   append_cross_time(l, r, time, False)
if exists_l and exists_x_fixed:
   append_cross_time(l, x_fixed, time, True)
if exists_r and exists_x_fixed:
   append_cross_time(x_fixed, r, time, True)
if exists_u and exists_d:
   append_cross_time(d, u, time, False)
if exists_d and exists_y_fixed:
   append_cross_time(d, y_fixed, time, True)
if exists_u and exists_y_fixed:
   append_cross_time(y_fixed, u, time, True)
time = list(time)
time.sort()

min_area = out_of_range * out_of_range
for t in time:
    dx = max(l[1] - t, r[1] + t, x_fixed[1]) - min(l[0] - t, r[0] + t, x_fixed[0])
    dy = max(d[1] - t, u[1] + t, y_fixed[1]) - min(d[0] - t, u[0] + t, y_fixed[0])
    min_area = min(dx * dy, min_area)

print(min_area)