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 = 10**20
max_Lx, max_Rx, max_UDx = -INF, -INF, -INF
min_Lx, min_Rx, min_UDx = INF, INF, INF
max_Uy, max_Dy, max_LRy = -INF, -INF, -INF
min_Uy, min_Dy, min_LRy = INF, INF, INF

for _ in range(N) :
    x, y, d = input().split()
    x, y = int(x), int(y)
    
    if d == 'L' :
        max_Lx = max(max_Lx, x)
        min_Lx = min(min_Lx, x)
        max_LRy = max(max_LRy, y)
        min_LRy = min(min_LRy, y)
    
    elif d == 'R' :
        max_Rx = max(max_Rx, x)
        min_Rx = min(min_Rx, x)
        max_LRy = max(max_LRy, y)
        min_LRy = min(min_LRy, y)
    
    elif d == 'U' :
        max_Uy = max(max_Uy, y)
        min_Uy = min(min_Uy, y)
        max_UDx = max(max_UDx, x)
        min_UDx = min(min_UDx, x)
    
    elif d == 'D':
        max_Dy = max(max_Dy, y)
        min_Dy = min(min_Dy, y)
        max_UDx = max(max_UDx, x)
        min_UDx = min(min_UDx, x)

def calc(t) :
    max_x = max(max_Lx-t, max_UDx, max_Rx+t)
    min_x = min(min_Lx-t, min_UDx, min_Rx+t)
    max_y = max(max_Dy-t, max_LRy, max_Uy+t)
    min_y = min(min_Dy-t, min_LRy, min_Uy+t)
    return (max_x - min_x) * (max_y - min_y)

schedule = [
    0, 
    max_UDx - max_Rx, max_Lx - max_UDx, (max_Lx - max_Rx) / 2,
    min_UDx - min_Rx, min_Lx - max_UDx, (min_Lx - min_Rx) / 2,
    max_LRy - max_Uy, max_Dy - max_LRy, (max_Dy - max_Uy) / 2,
    min_LRy - min_Uy, min_Dy - max_LRy, (min_Dy - min_Uy) / 2
]
min_diff = INF

for t in schedule :
    if 0 <= t < INF / 10 :
        min_diff = min(min_diff, calc(t))
    
print(min_diff)