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
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

import itertools

INF = 10**18
# R,L,U,D
data = {x:[-INF,INF,-INF,INF]for x in 'RLUD'}

N = int(readline())
XYD = read().split()
X = (int(x) for x in XYD[::3])
Y = (int(x) for x in XYD[1::3])
D = (x.decode('utf-8') for x in XYD[2::3])

for x,y,d in zip(X,Y,D):
    if data[d][0] < x: data[d][0] = x
    if data[d][1] > x: data[d][1] = x
    if data[d][2] < y: data[d][2] = y
    if data[d][3] > y: data[d][3] = y

X = []
Y = []
# a+tb
X += [(data['L'][0],-1), (data['L'][1],-1)]
X += [(data['R'][0],1), (data['R'][1],1)]
X += [(data['U'][0],0), (data['U'][1],0)]
X += [(data['D'][0],0), (data['D'][1],0)]

Y += [(data['L'][2],0), (data['L'][3],0)]
Y += [(data['R'][2],0), (data['R'][3],0)]
Y += [(data['U'][2],1), (data['U'][3],1)]
Y += [(data['D'][2],-1), (data['D'][3],-1)]

X = [(x,dx) for x,dx in X if abs(x) < INF]
Y = [(x,dx) for x,dx in Y if abs(x) < INF]

T = []
for (x,dx),(y,dy) in itertools.combinations(X,2):
    if dx == dy: continue
    # x + tdx = y + tdy
    T.append((x-y)/(dy-dx))
for (x,dx),(y,dy) in itertools.combinations(Y,2):
    if dx == dy: continue
    # x + tdx = y + tdy
    T.append((x-y)/(dy-dx))

T = set([0] + [t for t in T if t > 0])

def F(t):
    xs = [x+t*speed for x,speed in X]
    ys = [x+t*speed for x,speed in Y]
    dx = max(xs) - min(xs)
    dy = max(ys) - min(ys)
    return dx*dy

answer = min(F(t) for t in T)
print(answer)