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 copy

N = int(input())

U = []
D = []
R = []
L = []

for _ in range(N):
    x, y, ori = input().rstrip().split(' ')
    x = int(x)
    y = int(y)
    if ori == 'U':
        U.append([x, y])
    elif ori == 'D':
        D.append([x, y])
    elif ori == 'R':
        R.append([x, y])
    else:
        L.append([x, y])
      

def calc(inc_points, dec_points, other_points, index):
    inc = []
    dec = []
    other = [] 
    if len(inc_points) > 0:
        inc_min = min([x[index] for x in inc_points])
        inc_max = max([x[index] for x in inc_points])
        inc = [inc_min, inc_max]
    if len(dec_points) > 0:
        dec_min = min([x[index] for x in dec_points])
        dec_max = max([x[index] for x in dec_points])
        dec = [dec_min, dec_max]
    if len(other_points) > 0:
        other_min = min([x[index] for x in other_points])
        other_max = max([x[index] for x in other_points])
        other = [other_min, other_max]
       
    cross_time = [0]
    if len(inc_points) > 0 and len(dec_points) > 0:
        for u in [inc_min, inc_max]:
            for d in [dec_min, dec_max]:
                if u < d: # collision
                    cross_time.append((d - u) / 2)
                    
    if len(dec_points) > 0 and len(other_points) > 0:
        for rl in [other_min, other_max]:
            for d in [dec_min, dec_max]:
                if rl < d: # collision
                    cross_time.append(d - rl)
                    
    if len(inc_points) > 0 and len(other_points) > 0:
        for rl in [other_min, other_max]:
            for u in [inc_min, inc_max]:
                if u < rl: # collision
                    cross_time.append(rl - u)
                   
    return inc, dec, other, cross_time
    
def calc_size(inc, dec, other, times):
    sizes = []
    for time in times:
        values = copy.copy(other)
        if len(inc) > 0:
            values.extend([x + time for x in inc])
        if len(dec) > 0:
            values.extend([x - time for x in dec])
        sizes.append(max(values) - min(values))
    return sizes
   
inc_x, dec_x, other_x, cross_time_x = calc(R, L, U+D, 0)         
inc_y, dec_y, other_y, cross_time_y = calc(U, D, R+L, 1)

times = list(set(cross_time_x + cross_time_y))
sizes_x = calc_size(inc_x, dec_x, other_x, times)
sizes_y = calc_size(inc_y, dec_y, other_y, times)

print(min([x*y for x, y in zip(sizes_x, sizes_y)]))