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:

from itertools import combinations

INF = float("inf")
data = {d: [-INF, INF, -INF, INF] for d in 'RLUD'}

_, *XYD = open(0).read().split()
X = map(int, XYD[::3])
Y = map(int, XYD[1::3])
D = map(data.get, XYD[2::3])

for x, y, d in zip(X, Y, D):
    d[0] = max(d[0], x)
    d[1] = min(d[1], x)
    d[2] = max(d[2], y)
    d[3] = min(d[3], y)


X = [
    (data["L"][0], -1), (data["L"][1], -1),
    (data["R"][0], 1), (data["R"][1], 1),
    (data["U"][0], 0), (data["U"][1], 0),
    (data["D"][0], 0), (data["D"][1], 0),
]
Y = [
    (data["L"][2], 0), (data["L"][3], 0),
    (data["R"][2], 0), (data["R"][3], 0),
    (data["U"][2], 1), (data["U"][3], 1),
    (data["D"][2], -1), (data["D"][3], -1),
]

X = [(x, dx) for x, dx in X if abs(x) < INF]
Y = [(y, dy) for y, dy in Y if abs(y) < INF]

T = set(
    [0] +
    [max(0, (x - y) / (dy - dx)) for (x, dx), (y, dy) in combinations(X, 2) if dx != dy] +
    [max(0, (x - y) / (dy - dx)) for (x, dx), (y, dy) in combinations(Y, 2) if dx != dy]
)


def area(t):
    XX = [t * dx + x for x, dx in X]
    YY = [t * dy + y for y, dy in Y]

    dx = max(XX) - min(XX)
    dy = max(YY) - min(YY)

    return dx * dy


print(min(map(area, T)))