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:
def men(t):
    xmin = min(st + i * t for i, st in enumerate(mg[0]))
    xmax = max(st + i * t for i, st in enumerate(mg[1]))
    ymin = min(st + i * t for i, st in enumerate(ue[0]))
    ymax = max(st + i * t for i, st in enumerate(ue[1]))
    return (xmax - xmin) * (ymax - ymin)

n = int(input())
inf = 10**9
mg = [[inf, inf, inf], [-inf, -inf, -inf]]
ue = [[inf, inf, inf], [-inf, -inf, -inf]]
mg0=mg[0]
mg1=mg[1]
ue0=ue[0]
ue1=ue[1]
for _ in range(n):
    x, y, d = input().split()
    x = int(x)
    y = int(y)
    if d == "U":
        mv = 1
        uv = 2
    elif d == "D":
        mv = 1
        uv = 0
    elif d == "R":
        mv = 2
        uv = 1
    else:
        mv = 0
        uv = 1
    if x < mg0[mv]: mg0[mv] = x
    if x > mg1[mv]: mg1[mv] = x
    if y < ue0[uv]: ue0[uv] = y
    if y > ue1[uv]: ue1[uv] = y
t=set([0])
for lst in [mg0,mg1,ue0,ue1]:
    v0,v1,v2=lst
    for tk in [v0-v1,v1-v2,(v0-v2)/2]:
        if tk>=0:
            t.add(tk)
print(min(men(tk) for tk in t))