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())
xy = [[],[],[],[]]
s = {'L':0,'R':1,'U':2,'D':3}
for i in range(n):
  x,y,d = input().split()
  xy[s[d]] += [[int(x),int(y)]]
q = -10**9
p = [[q,q,q] for i in range(4)]
ss = [[0,2,1,1],[1,1,2,0]]
pm = [1,-1,1,-1]
for i in range(4):
  if xy[i]:
    for j in range(4):
      ps = ss[j//2][i]
      z = max(xy[i],key=lambda z:z[j//2]*pm[j])
      p[j][ps] = max(p[j][ps],z[j//2]*pm[j])
t = {0}
for i in range(4):
  z = [u*pm[i] for u in p[i]]
  t = t | {z[1]-z[2],z[0]-z[1],(z[0]-z[2])/2}
def dis(u,v):
  return max(p[0+v][0]-u,p[0+v][1],p[0+v][2]+u)-min(-p[1+v][0]-u,-p[1+v][1],-p[1+v][2]+u)
print(min([dis(u,0)*dis(u,2) for u in t if u<=2*10**8 and u>=0]))