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:
import sys


def check(t):
    maxx = max(ud_maxx, r_maxx + t, l_maxx - t)
    minx = min(ud_minx, r_minx + t, l_minx - t)
    maxy = max(lr_maxy, u_maxy + t, d_maxy - t)
    miny = min(lr_miny, u_miny + t, d_miny - t)
    return (maxx - minx) * (maxy - miny)


n = int(input())
lr_maxy, lr_miny, ud_maxx, ud_minx = -1e9, 1e9, -1e9, 1e9
l_maxx, l_minx, r_maxx, r_minx = -1e9, 1e9, -1e9, 1e9
u_maxy, u_miny, d_maxy, d_miny = -1e9, 1e9, -1e9, 1e9
for line in sys.stdin:
    x, y, d = line.rstrip().split()
    x, y = int(x), int(y)
    if d == 'L':
        lr_maxy = max(lr_maxy, y)
        lr_miny = min(lr_miny, y)
        l_maxx = max(l_maxx, x)
        l_minx = min(l_minx, x)
    elif d == 'R':
        lr_maxy = max(lr_maxy, y)
        lr_miny = min(lr_miny, y)
        r_maxx = max(r_maxx, x)
        r_minx = min(r_minx, x)
    elif d == 'U':
        ud_maxx = max(ud_maxx, x)
        ud_minx = min(ud_minx, x)
        u_maxy = max(u_maxy, y)
        u_miny = min(u_miny, y)
    else:
        ud_maxx = max(ud_maxx, x)
        ud_minx = min(ud_minx, x)
        d_maxy = max(d_maxy, y)
        d_miny = min(d_miny, y)

inflections = {0}
inflections.add(max(0, l_maxx - ud_maxx))
inflections.add(max(0, (l_maxx - r_maxx) / 2))
inflections.add(max(0, ud_maxx - r_maxx))
inflections.add(max(0, l_minx - ud_minx))
inflections.add(max(0, (l_minx - r_minx) / 2))
inflections.add(max(0, ud_minx - r_minx))

inflections.add(max(0, d_maxy - lr_maxy))
inflections.add(max(0, (d_maxy - u_maxy) / 2))
inflections.add(max(0, lr_maxy - u_maxy))
inflections.add(max(0, d_miny - lr_miny))
inflections.add(max(0, (d_miny - u_miny) / 2))
inflections.add(max(0, lr_miny - u_miny))

print(min(map(check, inflections)))