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())

x_fix_max = None
x_fix_min = None
x_inc_max = None
x_inc_min = None
x_dec_max = None
x_dec_min = None

y_fix_max = None
y_fix_min = None
y_inc_max = None
y_inc_min = None
y_dec_max = None
y_dec_min = None

for i in range(n):
    x, y, d = [a for a in input().split()]
    if d == "R":
        if x_inc_max is None or x_inc_max < int(x):
            x_inc_max = int(x)
        if x_inc_min is None or x_inc_min > int(x):
            x_inc_min = int(x)
        if y_fix_max is None or y_fix_max < int(y):
            y_fix_max = int(y)
        if y_fix_min is None or y_fix_min > int(y):
            y_fix_min = int(y)
    if d == "L":
        if x_dec_max is None or x_dec_max < int(x):
            x_dec_max = int(x)
        if x_dec_min is None or x_dec_min > int(x):
            x_dec_min = int(x)
        if y_fix_max is None or y_fix_max < int(y):
            y_fix_max = int(y)
        if y_fix_min is None or y_fix_min > int(y):
            y_fix_min = int(y)
    if d == "U":
        if y_inc_max is None or y_inc_max < int(y):
            y_inc_max = int(y)
        if y_inc_min is None or y_inc_min > int(y):
            y_inc_min = int(y)
        if x_fix_max is None or x_fix_max < int(x):
            x_fix_max = int(x)
        if x_fix_min is None or x_fix_min > int(x):
            x_fix_min = int(x)
    if d == "D":
        if y_dec_max is None or y_dec_max < int(y):
            y_dec_max = int(y)
        if y_dec_min is None or y_dec_min > int(y):
            y_dec_min = int(y)
        if x_fix_max is None or x_fix_max < int(x):
            x_fix_max = int(x)
        if x_fix_min is None or x_fix_min > int(x):
            x_fix_min = int(x)

if x_inc_min is None:
    x_inc_min = 10 ** 10
if x_dec_min is None:
    x_dec_min = 10 ** 10
if x_fix_min is None:
    x_fix_min = 10 ** 10
if x_inc_max is None:
    x_inc_max = -10 ** 10
if x_dec_max is None:
    x_dec_max = -10 ** 10
if x_fix_max is None:
    x_fix_max = -10 ** 10
if y_inc_min is None:
    y_inc_min = 10 ** 10
if y_dec_min is None:
    y_dec_min = 10 ** 10
if y_fix_min is None:
    y_fix_min = 10 ** 10
if y_inc_max is None:
    y_inc_max = -10 ** 10
if y_dec_max is None:
    y_dec_max = -10 ** 10
if y_fix_max is None:
    y_fix_max = -10 ** 10

t_list = [0]
t_list += [-x_inc_max + x_fix_max, x_dec_max - x_fix_max, (x_dec_max - x_inc_max) / 2]
t_list += [-y_inc_max + y_fix_max, y_dec_max - y_fix_max, (y_dec_max - y_inc_max) / 2]
t_list += [-x_inc_min + x_fix_min, x_dec_min - x_fix_min, (x_dec_min - x_inc_min) / 2]
t_list += [-y_inc_min + y_fix_min, y_dec_min - y_fix_min, (y_dec_min - y_inc_min) / 2]


min_mult = None
for t in t_list:
    if t < 0:
        continue
    x_max = max(x_inc_max + t, x_fix_max, x_dec_max - t)
    x_min = min(x_inc_min + t, x_fix_min, x_dec_min - t)
    y_max = max(y_inc_max + t, y_fix_max, y_dec_max - t)
    y_min = min(y_inc_min + t, y_fix_min, y_dec_min - t)
    mult = (x_max - x_min) * (y_max - y_min)
    if min_mult is None or min_mult > mult:
        min_mult = mult
print(str(min_mult))