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
from itertools import product
n=int(input())
Rx,Ry,Lx,Ly,Ux,Uy,Dx,Dy=[],[],[],[],[],[],[],[]
for _ in range(n):
    x,y,d=input().split()
    x=int(x); y=int(y)
    if d=='R':
        Rx.append(x); Ry.append(y)
    elif d=='L':
        Lx.append(x); Ly.append(y)
    elif d=='U':
        Ux.append(x); Uy.append(y)
    else:
        Dx.append(x); Dy.append(y)
inf=float('inf')
stay_x=[min(Ux+Dx+[inf]),max(Ux+Dx+[-inf])]
plus_x=[min(Rx+[inf]),max(Rx+[-inf])]
minus_x=[min(Lx+[inf]),max(Lx+[-inf])]
plus_y=[min(Uy+[inf]),max(Uy+[-inf])]
minus_y=[min(Dy+[inf]),max(Dy+[-inf])]
stay_y=[min(Ly+Ry+[inf]),max(Ly+Ry+[-inf])]

T=[0]
for x1,x2 in product(minus_x,plus_x):
    if x1 in (-inf,inf) or x2 in (-inf,inf):
        continue
    t=(x1-x2)/2
    if t>0:
        T.append(t)
for x1,x2 in product(minus_x,stay_x):
    if x1 in (-inf,inf) or x2 in (-inf,inf):
        continue
    t=x1-x2
    if t>0:
        T.append(t)
for x1,x2 in product(plus_x,stay_x):
    if x1 in (-inf,inf) or x2 in (-inf,inf):
        continue
    t=x2-x1
    if t>0:
        T.append(t)
for y1,y2 in product(minus_y,plus_y):
    if y1 in (-inf,inf) or y2 in (-inf,inf):
        continue
    t=(y1-y2)/2
    if t>0:
        T.append(t)
for y1,y2 in product(minus_y,stay_y):
    if y1 in (-inf,inf) or y2 in (-inf,inf):
        continue
    t=y1-y2
    if t>0:
        T.append(t)
for y1,y2 in product(plus_y,stay_y):
    if y1 in (-inf,inf) or y2 in (-inf,inf):
        continue
    t=y2-y1
    if t>0:
        T.append(t)
T=sorted(set(T))
T.append(10**10)

def width(t):
    left=min(stay_x[0],plus_x[0]+t,minus_x[0]-t)
    right=max(stay_x[1],plus_x[1]+t,minus_x[1]-t)
    return right-left
def height(t):
    down=min(stay_y[0],plus_y[0]+t,minus_y[0]-t)
    up=max(stay_y[1],plus_y[1]+t,minus_y[1]-t)
    return up-down

def minS(x1,x2,y1,y2):
    ax,bx=x2-x1,x1; ay,by=y2-y1,y1
    a,b,c=ax*ay,ax*by+bx*ay,bx*by
    if a<=0:
        return min(x1*y1,x2*y2)
    m=-b/(2*a)
    if m<0 or m>1:
        return min(x1*y1,x2*y2)
    return a*m**2+b*m+c

l=len(T)
X=[width(t) for t in T]
Y=[height(t) for t in T]
ans=inf
for i in range(l-1):
    x1,x2=X[i],X[i+1]
    y1,y2=Y[i],Y[i+1]
    ans=min(ans,minS(x1,x2,y1,y2))
print(ans)