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

N=int(input())
P=[input().split() for i in range(N)]

for i in range(N):
    P[i][0]=int(P[i][0])
    P[i][1]=int(P[i][1])

def ans(Q):
    MINX=10**15
    MAXX=-10**15
    MINY=10**15
    MAXY=-10**15

    for x,y in Q:
        MINX=min(MINX,x)
        MINY=min(MINY,y)
        MAXX=max(MAXX,x)
        MAXY=max(MAXY,y)

    return (MAXX-MINX)*(MAXY-MINY)
    
def time(t):
    Q=[]
    for x,y,s in P:
        if s=="R":
            x+=t
        elif s=="L":
            x-=t
        elif s=="U":
            y+=t
        else:
            y-=t
        Q.append([x,y])

    return Q

MIN=0
MAX=10**10

while MAX-MIN>=1:
    #print(MAX,MIN)
    x=(MIN+MAX)//2

    if ans(time(x))>ans(time(x+1/2)):
        MIN=x+1/2
    else:
        MAX=x

        
print(min(ans(time(MAX)),ans(time(MIN))))