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:
from collections import defaultdict
N=int(input())

xdic=defaultdict(set)
ydic=defaultdict(set)
for i in range(N):
  xs,ys,d=input().split()
  x=int(xs)
  y=int(ys)
  if d=="L":
    xdic[-1].add(x)
    ydic[0].add(y)
  elif d=="R":
    xdic[1].add(x)
    ydic[0].add(y)
  elif d=="U":
    xdic[0].add(x)
    ydic[1].add(y)
  else:
    xdic[0].add(x)
    ydic[-1].add(y)

xset=set()
for d in [-1,0,1]:
  if len(xdic[d]):
    min_d=min(xdic[d])
    max_d=max(xdic[d])
    xset.add((min_d,d))
    xset.add((max_d,d))
  
yset=set()
for d in [-1,0,1]:
  if len(ydic[d]):
    min_d=min(ydic[d])    
    max_d=max(ydic[d])
    yset.add((min_d,d))
    yset.add((max_d,d))

def cand_time(plist):
  ret=set()
  for i in range(len(plist)):
    p1,d1=plist[i]
    for j in range(i+1,len(plist)):
      p2,d2=plist[j]
      if d1==d2:
        continue
        
      if d1==-1:
        if d2==0:
          t=p1-p2
        else:
          t=(p1-p2)/2
      elif d1==0:
        if d2==-1:
          t=p2-p1
        else:
          t=p1-p2
      else:
        if d2==-1:
          t=(p2-p1)/2
        else:
          t=p2-p1
       
      if t>0:
        ret.add(t)
  return ret

cand_time_x=cand_time(list(xset))
cand_time_y=cand_time(list(yset))
#print(cand_time_x,cand_time_y)
cand_t=[0]+list(cand_time_x)+list(cand_time_y)
#print(cand_t)

def get_pos(pd,t):
  p,d=pd
  return p+d*t

answer=float("inf")
for t in cand_t:
  pos_min_x=float("inf")
  pos_max_x=-float("inf")
  for x2 in xset:
    pos_min_x=min(pos_min_x,get_pos(x2,t))
    pos_max_x=max(pos_max_x,get_pos(x2,t))
    
  pos_min_y=float("inf")
  pos_max_y=-float("inf")
  for y2 in yset:
    pos_min_y=min(pos_min_y,get_pos(y2,t))
    pos_max_y=max(pos_max_y,get_pos(y2,t))

  #print(t,pos_min_x,pos_max_x,pos_min_y,pos_max_y)
  t_ans=abs(pos_max_x-pos_min_x)*abs(pos_max_y-pos_min_y)
  if answer>=t_ans:
    answer=t_ans
    #print(answer,t,abs(pos_max_x-pos_min_x),abs(pos_max_y-pos_min_y))
  
print(answer)