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())
points=[]
ds=[]
for i in range(N):
  x,y,d=input().split()
  x,y=map(int,(x,y))
  if d=='L':d=(-1,0)
  if d=='R':d=(1,0)
  if d=='U':d=(0,1)
  if d=='D':d=(0,-1)
  points.append((x,y))
  ds.append(d)

if N==1:
  print(0)
  exit()

x,y=list(zip(*points))
xmax,xmin,ymax,ymin=max(x),min(x),max(y),min(y)

def region(p):
  x,y=list(zip(*p))
  return (max(x)-min(x))*(max(y)-min(y))

def process(p,d,second=1):
  return [(p[i][0]+second*d[i][0],p[i][1]+second*d[i][1]) for i in range(N)]

def func(x):
  return region(process(points,ds,x))

def ternary_search(f, x_min, x_max, epsilon=1e-15):
    while True:
        x1,x2 = 1/3*(x_max-x_min)+x_min,2/3*(x_max-x_min)+x_min
        gap = f(x1)-f(x2)
        if gap < 0: x_max=x2
        else: x_min=x1
        if abs(gap) <= epsilon:break
    return (x_max+x_min)/2
  
t_max=4*(max(xmax-xmin,ymax-ymin))
t_min=0

x_opt = ternary_search(func, t_min, t_max, epsilon=1e-15)

print(func(x_opt))