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())

static_min_x = 10 ** 8
static_max_x = - 10 ** 8
static_min_y = 10 ** 8
static_max_y = - 10 ** 8
rx_max = - 10 ** 8
rx_min = 10 ** 8
lx_max = - 18 ** 8
lx_min = 10 ** 8
uy_max = - 10 ** 8
uy_min = 10 ** 8
dy_max = - 18 ** 8
dy_min = 10 ** 8
for _ in range(n):
    x, y, d = input().split()
    x = int(x)
    y = int(y)
    if d == 'R':
        rx_max = max(rx_max, x)
        rx_min = min(rx_min, x)
        static_max_y = max(static_max_y, y)
        static_min_y = min(static_min_y, y)
    elif d == 'L':
        lx_max = max(lx_max, x)
        lx_min = min(lx_min, x)
        static_max_y = max(static_max_y, y)
        static_min_y = min(static_min_y, y)
    elif d == 'U':
        uy_max = max(uy_max, y)
        uy_min = min(uy_min, y)
        static_max_x = max(static_max_x, x)
        static_min_x = min(static_min_x, x)
    else:
        dy_max = max(dy_max, y)
        dy_min = min(dy_min, y)
        static_max_x = max(static_max_x, x)
        static_min_x = min(static_min_x, x)

def calc_ans(t):
    max_x = max(rx_max + t, lx_max - t, static_max_x)
    min_x = min(rx_min + t, lx_min - t, static_min_x)
    max_y = max(uy_max + t, dy_max - t, static_max_y)
    min_y = min(uy_min + t, dy_min - t, static_min_y)
    return (max_x - min_x) * (max_y - min_y)

ans = calc_ans(0)
ans = min(ans, calc_ans(abs(rx_max - lx_max) / 2.0))
if lx_max > static_max_x:
    ans = min(ans, calc_ans(lx_max - static_max_x))
if static_max_x > rx_max:
    ans = min(ans, calc_ans(static_max_x - rx_max))

ans = min(ans, calc_ans(abs(rx_min - lx_min) / 2.0))
if lx_min > static_min_x:
    ans = min(ans, calc_ans(lx_min - static_min_x))
if static_min_x > rx_min:
    ans = min(ans, calc_ans(static_min_x - rx_min))

ans = min(ans, calc_ans(abs(uy_max - dy_max) / 2.0))
if dy_max > static_max_y:
    ans = min(ans, calc_ans(dy_max - static_max_y))
if static_max_y > uy_max:
    ans = min(ans, calc_ans(static_max_y - uy_max))

ans = min(ans, calc_ans(abs(uy_min - dy_min) / 2.0))
if dy_min > static_min_y:
    ans = min(ans, calc_ans(dy_min - static_min_y))
if static_min_y > uy_min:
    ans = min(ans, calc_ans(static_min_y - uy_min))

print(ans)