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:
#!/usr/bin/python3
# -*- coding: utf-8 -*-
from decimal import *


N = int(input())
nmove_x = [10**9, -10**9] ##[min,max]
nmove_y = [10**9, -10**9] ##[min,max]
move = {"U":[10**9, -10**9], "D":[10**9, -10**9], "R":[10**9, -10**9], "L":[10**9, -10**9]}

for _ in range(N):
  x,y,d = map(str, input().split())
  x,y = [int(x),int(y)]
  if d in "UD":
    move[d] = [min([move[d][0],y]),max([move[d][1],y])]
    nmove_x = [min([nmove_x[0],x]),max([nmove_x[1],x])]
  else:
    move[d] = [min([move[d][0],x]),max([move[d][1],x])]
    nmove_y = [min([nmove_y[0],y]),max([nmove_y[1],y])]


def get_bb(t):
  x_mx = max([move["R"][1]+t,move["L"][1]-t,nmove_x[1]])
  x_mn = min([move["R"][0]+t,move["L"][0]-t,nmove_x[0]])
  y_mx = max([move["U"][1]+t,move["D"][1]-t,nmove_y[1]])
  y_mn = min([move["U"][0]+t,move["D"][0]-t,nmove_y[0]])
  return ((x_mx-x_mn)*(y_mx-y_mn))


## にぶたん！
l,r = [Decimal("0"),Decimal("10000000000")]
for _ in range(500):
  m = Decimal(l+r)/2
  if get_bb(m-Decimal("0.00000001")) < get_bb(m+Decimal("0.00000001")):
    r = m
  else:
    l = m
print(get_bb(m))