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())
x1, x2, y1, y2 = {}, {}, {}, {}
INF = 10 ** 10

for i in range(N):
    x, y, d = input().split()
    x, y = int(x) * 2, int(y) * 2

    def update_x(v, x):
        if v not in x1:
            x1[v] = x2[v] = x
        else:
            x1[v] = min(x1[v], x)
            x2[v] = max(x2[v], x)

    def update_y(v, y):
        if v not in y1:
            y1[v] = y2[v] = y
        else:
            y1[v] = min(y1[v], y)
            y2[v] = max(y2[v], y)

    if d == 'R':
        update_x(+1, x)
        update_y(0, y)
    elif d == 'L':
        update_x(-1, x)
        update_y(0, y)
    elif d == 'U':
        update_x(0, x)
        update_y(+1, y)
    elif d == 'D':
        update_x(0, x)
        update_y(-1, y)

def area(t):
    xmin, xmax, ymin, ymax = INF, -INF, INF, -INF
    for (v, x) in x1.items():
        xmin = min(xmin, x + v * t)
    for (v, x) in x2.items():
        xmax = max(xmax, x + v * t)
    for (v, y) in y1.items():
        ymin = min(ymin, y + v * t)
    for (v, y) in y2.items():
        ymax = max(ymax, y + v * t)
    return (xmax - xmin) * (ymax - ymin)

ans = area(0)

x3 = list(x1.items()) + list(x2.items())
for i in range(len(x3)):
    for j in range(i + 1, len(x3)):
        if x3[i][0] != x3[j][0]:
            t = (x3[j][1] - x3[i][1]) // (x3[i][0] - x3[j][0])
            if t >= 0:
                ans = min(ans, area(t))

y3 = list(y1.items()) + list(y2.items())
for i in range(len(y3)):
    for j in range(i + 1, len(y3)):
        if y3[i][0] != y3[j][0]:
            t = (y3[j][1] - y3[i][1]) // (y3[i][0] - y3[j][0])
            if t >= 0:
                ans = min(ans, area(t))

print(ans / 4)