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:
# coding: utf-8
# Your code here!

import sys
n = int(input())
inf = float("inf")
xmin = [inf, inf, inf] #傾き-1,0,1
xmax = [-inf, -inf, -inf]
ymin = [inf, inf, inf]
ymax = [-inf, -inf, -inf]

for _ in range(n):
    x,y,d = [i for i in input().split()]
    x=int(x); y=int(y)
    if d=="U": ud = 2; lr = 1
    if d=="D": ud = 0; lr = 1
    if d=="L": ud = 1; lr = 0
    if d=="R": ud = 1; lr = 2
    xmin[lr] = min(xmin[lr],x)
    xmax[lr] = max(xmax[lr],x)
    ymin[ud] = min(ymin[ud],y)
    ymax[ud] = max(ymax[ud],y)

def lpos(t):
    return min([(v-1)*t + i for v,i in enumerate(xmin)])
def rpos(t):
    return max([(v-1)*t + i for v,i in enumerate(xmax)])
def dpos(t):
    return min([(v-1)*t + i for v,i in enumerate(ymin)])
def upos(t):
    return max([(v-1)*t + i for v,i in enumerate(ymax)])


s = {0}
for i in range(3):
    for j in range(i+1,3):
        t = (xmin[j]-xmin[i])/(i-j)
        if t > 0 and t != inf and t!= -inf: s.add(t)
        t = (xmax[j]-xmax[i])/(i-j)
        if 0 < t and t != inf and t!= -inf: s.add(t)
        t = (ymin[j]-ymin[i])/(i-j)
        if 0 < t and t != inf and t!= -inf: s.add(t)
        t = (ymax[j]-ymax[i])/(i-j)
        if 0 < t and t != inf and t!= -inf: s.add(t)
        

ans = 10**18
for t in s:
    area = (rpos(t)-lpos(t))*(upos(t)-dpos(t))
    if area < ans: ans = area

print(ans)