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:
INF = 10**18


def calc(point_list, t):
    x_min, y_min, x_max, y_max = INF, INF, -INF, -INF
    for point in point_list:
        x, y, d = point
        dx = t if d == 'R' else (-t if d == 'L' else 0)
        dy = t if d == 'U' else (-t if d == 'D' else 0)
        x_min = min(x_min, x + dx)
        x_max = max(x_max, x + dx)
        y_min = min(y_min, y + dy)
        y_max = max(y_max, y + dy)
    return (x_max - x_min) * (y_max - y_min)


def main():
    N = int(input())
    point_list = list()
    x_min, y_min, x_max, y_max = INF, INF, -INF, -INF
    for _ in range(N):
        X, Y, D = input().split()
        X = int(X)
        x_min = min(x_min, X)
        x_max = max(x_max, X)
        Y = int(Y)
        y_min = min(y_min, Y)
        y_max = max(y_max, Y)
        point_list.append((X, Y, D))
    if N == 1:
        print(0)
        return
    t_left, t_right = 0, 2 * max(x_max - x_min, y_max - y_min)
    v_left, v_right = calc(point_list, t_left), calc(point_list, t_right)
    while True:
        dt = t_right - t_left
        if dt < 10 ** (-8):
            break
        t_in_left, t_in_right = t_left + dt / 3, t_right - dt / 3
        v_in_left, v_in_right = calc(point_list, t_in_left), calc(point_list, t_in_right)
        if v_in_left < v_in_right:
            t_right = t_in_right
            v_right = v_in_right
        else:
            t_left = t_in_left
            v_left = v_in_left
    print(v_left)


if __name__ == '__main__':
    main()