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:
import sys
input = sys.stdin.readline
N = int(input())
a = []
l = []
r = []
lr = []
u = []
d = []
ud = []
for _ in range(N):
  x, y, w = input().split()
  x, y = map(int, (x, y))
  a.append((x, y, w))

  if w == "L":
    l.append(x)
    ud.append(y)
  if w == "R":
    r.append(x)
    ud.append(y)
  if w == "U":
    u.append(y)
    lr.append(x)
  if w == "D":
    d.append(y)
    lr.append(x)

l.sort()
r.sort()
lr.sort()
u.sort()
d.sort()
ud.sort()

t = [0]
if len(l):
  if len(r): t.append((l[-1] - r[-1]) / 2)
  if len(lr):
    t.append(l[-1] - lr[-1])
    t.append(l[0] - lr[0])
if len(r):
  if len(l): t.append((l[0] - r[0]) / 2)
  if len(lr):
    t.append(lr[0] - r[0])
    t.append(lr[-1] - r[-1])
if len(d):
  if len(u): t.append((d[-1] - u[-1]) / 2)
  if len(ud):
    t.append(d[-1] - ud[-1])
    t.append(d[0] - ud[0])
if len(u):
  if len(d): t.append((d[0] - u[0]) / 2)
  if len(ud):
    t.append(ud[0] - u[0])
    t.append(ud[-1] - u[-1])

t = sorted(set(t), reverse = True)
while t[-1] < 0: t.pop()

def solve(tt):
  ll = float("inf")
  rr = -float("inf")
  uu = -float("inf")
  dd = float("inf")
  for x, y, w in a:
    xx = x
    yy = y
    if w == "L": xx -= tt
    if w == "R": xx += tt
    if w == "U": yy += tt
    if w == "D": yy -= tt
    ll = min(ll, xx)
    rr = max(rr, xx)
    uu = max(uu, yy)
    dd = min(dd, yy)
  return (rr - ll) * (uu - dd)

res = float("inf")
for tt in t: res = min(res, solve(tt))
print(res)