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 PYTHON):

Solution:
import itertools as ite
import math
import random

INF = 10 ** 18
MOD = 10 ** 9 + 7

dx_ = [-1, 1, 0, 0]
dy_ = [0, 0, -1, 1]

m = {"L" : 0, "R" : 1, "D" : 2, "U" : 3}

N = input()
ls = []
ts = [0]

x1 = x2 = x3 = y1 = y2 = y3 = -INF

for loop in range(N):
    x, y, d = raw_input().split()
    x, y = int(x), int(y)
    d = m[d]
    ls += [(x, y, d)]
    if d == 0:
        x1 = max(x1, x)
        y2 = max(y2, y)
    if d == 1:
        x3 = max(x3, x)
        y2 = max(y2, y)
    if d == 2:
        x2 = max(x2, x)
        y1 = max(y1, y)
    if d == 3:
        x2 = max(x2, x)
        y3 = max(y3, y)
ts += [x1 - x2, x2 - x3, (x1 - x3) / 2.0]
ts += [y1 - y2, y2 - y3, (y1 - y3) / 2.0]

x1 = x2 = x3 = y1 = y2 = y3 = -INF

for x, y, d in ls:
    x, y = -x, -y
    d = d / 2 * 2 + (d % 2 == 0)
    if d == 0:
        x1 = max(x1, x)
        y2 = max(y2, y)
    if d == 1:
        x3 = max(x3, x)
        y2 = max(y2, y)
    if d == 2:
        x2 = max(x2, x)
        y1 = max(y1, y)
    if d == 3:
        x2 = max(x2, x)
        y3 = max(y3, y)
ts += [x1 - x2, x2 - x3, (x1 - x3) / 2.0]
ts += [y1 - y2, y2 - y3, (y1 - y3) / 2.0]

ans = INF

for t in ts:
    if t < 0 or t > 10 ** 10:
        continue
    x1 = y1 = INF
    x2 = y2 = -INF
    for x, y, d in ls:
        dx, dy = dx_[d], dy_[d]
        X = x + dx * t
        Y = y + dy * t
        x1 = min(x1, X)
        x2 = max(x2, X)
        y1 = min(y1, Y)
        y2 = max(y2, Y)
    ans = min(ans, (x2 - x1) * (y2 - y1))
print "%.12f" % ans