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())
xyd = [list(input().split()) for i in range(n)]
xmax,ymax = [-10**9,-10**9,-10**9],[-10**9,-10**9,-10**9]
xmin,ymin = [10**9,10**9,10**9],[10**9,10**9,10**9]
#xmax: max(x1-t,x2,x3+t)
#xmin: min(x1+t,x2,x3-t)
#ymax: max(y1-t,y2,y3+t)
#ymin: min(y1+t,y2,y3-t)
def chp(ls,a,flg1,i):
  if flg1:
    ls[i] = max(ls[i],a)
  else:
    ls[i] = min(ls[i],a)
def area(t):
  x = max(xmax[0]-t,xmax[1],xmax[2]+t)-min(xmin[0]+t,xmin[1],xmin[2]-t)
  y = max(ymax[0]-t,ymax[1],ymax[2]+t)-min(ymin[0]+t,ymin[1],ymin[2]-t)
  return x*y
for x,y,d in xyd:
  x,y = int(x),int(y)
  if d in ("L","R"):
    chp(ymax,y,1,1)
    chp(ymin,y,0,1)
    if d == "R":
      chp(xmin,x,0,0)
      chp(xmax,x,1,2)
    if d == "L":
      chp(xmin,x,0,2)
      chp(xmax,x,1,0)
  elif d in ("U","D"):
    chp(xmax,x,1,1)
    chp(xmin,x,0,1)
    if d == "U":
      chp(ymax,y,1,2)
      chp(ymin,y,0,0)
    if d == "D":
      chp(ymin,y,0,2)
      chp(ymax,y,1,0)

event = [0]
for ls in xmax,ymax:
  event.append(ls[0]-ls[1])
  event.append((ls[0]-ls[2])/2)
  event.append(ls[1]-ls[2])
for ls in xmin,ymin:
  event.append(ls[1]-ls[0])
  event.append((ls[2]-ls[0])/2)
  event.append(ls[2]-ls[1])
ans = 10**18

for i in event:
  if i>=0:
    for j in range(-10,10):
      if i+j*0.5 >= 0:
        ans = min(ans,area(i+j*0.5))
print(ans)