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())
r,l,u,d=[[] for _ in range(4)]
cx_max,cx_min,cy_max,cy_min=[None for _ in range(4)]

for i in range(n):
    x,y,s=input().split()
    x,y=int(x),int(y)
    if s=='R':
        r.append(x)
        if cy_max==None or cy_min==None:
            cy_max,cy_min=y,y
        cy_max,cy_min=max(cy_max,y),min(cy_min,y)
    if s=='L':
        l.append(x)
        if cy_max==None or cy_min==None:
            cy_max,cy_min=y,y
        cy_max,cy_min=max(cy_max,y),min(cy_min,y)

    if s=='U':
        u.append(y)
        if cx_max==None or cx_min==None:
            cx_max,cx_min=x,x
        cx_max,cx_min=max(cx_max,x),min(cx_min,x)
    if s=='D':
        d.append(y)
        if cx_max==None or cx_min==None:
            cx_max,cx_min=x,x
        cx_max,cx_min=max(cx_max,x),min(cx_min,x)
        
r.sort()
l.sort()
u.sort()
d.sort()

T=[0,10**9]
for j in r+l:
    if cx_max!=None:
        T.append(abs(j-cx_min))
        T.append(abs(j-cx_max))
for j in u+d:
    if cy_max!=None:
        T.append(abs(j-cy_min))
        T.append(abs(j-cy_max))

try:
    for i in [r[0],r[-1]]:
        for j in [l[0],l[-1]]:
            T.append(abs(i-j)/2)
except:
    0
try:
    for i in [u[0],u[-1]]:
        for j in [d[0],d[-1]]:
            T.append(abs(i-j)/2)
except:
    0

def val(t):
    xmax,xmin,ymax,ymin=[[] for _ in range(4)]
    if u:
        ymax.append(u[-1]+t)
        ymin.append(u[0]+t)
    if d:
        ymax.append(d[-1]-t)
        ymin.append(d[0]-t)
    if cy_max!=None:
        ymax.append(cy_max)
        ymin.append(cy_min)
        
    if r:
        xmax.append(r[-1]+t)
        xmin.append(r[0]+t)
    if l:
        xmax.append(l[-1]-t)
        xmin.append(l[0]-t)
    if cx_max!=None:
        xmax.append(cx_max)
        xmin.append(cx_min)
    
    Y=max(ymax)-min(ymin)
    X=max(xmax)-min(xmin)
    return X*Y

ans=val(0)
for t in T:
    ans=min(ans,val(t))
    
print(ans)