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
sys.setrecursionlimit(2147483647)
INF=10**9
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def resolve():
    n=int(input())
    X=[[INF,-INF] for _ in range(3)]
    Y=[[INF,-INF] for _ in range(3)]
    for _ in range(n):
        x,y,d=input().split()
        x=int(x); y=int(y)
        if(d=='R'):
            X[2][0]=min(X[2][0],x)
            X[2][1]=max(X[2][1],x)
            Y[1][0]=min(Y[1][0],y)
            Y[1][1]=max(Y[1][1],y)
        elif(d=='L'):
            X[0][0]=min(X[0][0],x)
            X[0][1]=max(X[0][1],x)
            Y[1][0]=min(Y[1][0],y)
            Y[1][1]=max(Y[1][1],y)
        elif(d=='U'):
            X[1][0]=min(X[1][0],x)
            X[1][1]=max(X[1][1],x)
            Y[2][0]=min(Y[2][0],y)
            Y[2][1]=max(Y[2][1],y)
        elif(d=='D'):
            X[1][0]=min(X[1][0],x)
            X[1][1]=max(X[1][1],x)
            Y[0][0]=min(Y[0][0],y)
            Y[0][1]=max(Y[0][1],y)

    T=[0]
    for i in range(3):
        for j in range(i): # i>j
            t=-(X[i][0]-X[j][0])/(i-j)
            if(t>0): T.append(t)
            t=-(X[i][1]-X[j][1])/(i-j)
            if(t>0): T.append(t)
            t=-(Y[i][0]-Y[j][0])/(i-j)
            if(t>0): T.append(t)
            t=-(Y[i][1]-Y[j][1])/(i-j)
            if(t>0): T.append(t)

    def f(t):
        x_min=min(X[0][0],X[1][0]+t,X[2][0]+2*t)
        x_max=max(X[0][1],X[1][1]+t,X[2][1]+2*t)
        y_min=min(Y[0][0],Y[1][0]+t,Y[2][0]+2*t)
        y_max=max(Y[0][1],Y[1][1]+t,Y[2][1]+2*t)
        return (x_max-x_min)*(y_max-y_min)

    ans=float("inf")
    for t in T:
        ans=min(ans,f(t))
    print(ans)
resolve()