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())
inf=float("inf")
data=[[inf,-inf,inf,-inf] for i in range(4)]
dic={ "U" : 0 , "D" : 1 , "R" : 2 , "L" : 3 }

for i in range(N):
    x,y,d=input().split()
    x,y=int(x),int(y)
    u=data[dic[d]]
    u[0]=min(u[0],x)
    u[1]=max(u[1],x)
    u[2]=min(u[2],y)
    u[3]=max(u[3],y)

a,b,c,d=data[0]
e,f,g,h=data[1]
i,j,k,l=data[2]
m,n,o,p=data[3]

a=min(a,e)
b=max(b,f)
k=min(k,o)
l=max(l,p)

if a==inf:
    a=-inf
    b=inf

time=[0]
time.append(a-i)
time.append(m-a)
time.append((m-i)/2)
time.append(b-j)
time.append(n-b)
time.append((n-j)/2)
time.append(k-c)
time.append(g-k)
time.append((g-c)/2)
time.append(l-d)
time.append(h-l)
time.append((h-d)/2)

ans=inf
for t in time:
    if 0<=t<=10**10:
        lst=[]
        for u in data:
            lst.append(u[:])
        lst[2][0]+=t
        lst[2][1]+=t
        lst[0][2]+=t
        lst[0][3]+=t
        lst[3][0]-=t
        lst[3][1]-=t
        lst[1][2]-=t
        lst[1][3]-=t
        
        lsls=[]
        for j in range(4):
            if j%2==0:
                m=inf
                for i in range(4):
                    m=min(m,lst[i][j])
                lsls.append(m)
            else:
                M=-inf
                for i in range(4):
                    M=max(M,lst[i][j])
                lsls.append(M)
        ans=min(ans,(lsls[1]-lsls[0])*(lsls[3]-lsls[2]))

print(ans)