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:
N=int(input())
table=[]
for i in range(N):
    x,y,d=input().split()
    x,y=int(x),int(y)
    table.append((x,y,d))
anspos=[0]
inf=10**10
a=-inf
b=-inf
c=-inf
for i in range(N):
    x,y,d=table[i]
    if d=='L':
        a=max(x,a)
    elif d=='R':
        b = max(x, b)
    else:
        c = max(x, c)
#anspos+=[(a+b)/2,(b+c)/2,(c+a)/2]
#anspos+=[max( (a-b)/2,0),max((b-a)/2,0),max(c-a,0),max(a-c,0),max(abs(b-c),0),max(c-b,0)]
anspos+=[abs(a-b)/2,abs(a-c),abs(b-c)]
a=inf
b=inf
c=inf
for i in range(N):
    x,y,d=table[i]
    if d=='L':
        a=min(x,a)
    elif d=='R':
        b = min(x, b)
    else:
        c = min(x, c)
anspos+=[abs(a-b)/2,abs(a-c),abs(b-c)]
a=-inf
b=-inf
c=-inf
for i in range(N):
    x,y,d=table[i]
    if d=='U':
        a=max(y,a)
    elif d=='D':
        b = max(y, b)
    else:
        c = max(y, c)
anspos+=[abs(a-b)/2,abs(a-c),abs(b-c)]
a=inf
b=inf
c=inf
for i in range(N):
    x,y,d=table[i]
    if d=='D':
        a=min(y,a)
    elif d=='U':
        b = min(y, b)
    else:
        c = min(y, c)
ans=10**30
anspos+=[abs(a-b)/2,abs(a-c),abs(b-c)]
#print(anspos)
for t in anspos:
    xmax=-inf
    xmin=inf
    ymax=-inf
    ymin=inf
    for i in range(N):
        x, y, d = table[i]
        if d=='U':
            y+=t
        elif d=='D':
            y-=t
        elif d=='L':
            x-=t
        elif d=='R':
            x+=t
        xmax=max(xmax,x)
        xmin = min(xmin, x)
        ymax = max(ymax, y)
        ymin = min(ymin, y)
    kai=(xmax-xmin)*(ymax-ymin)
    #print(kai,t)
    ans=min(ans,kai)
print(ans)