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())
lm = [float("INF")]*3
rm = [-float("INF")]*3
um = [-float("INF")]*3
dm = [float("INF")]*3

for i in range(N):
    x,y,d = input().split()
    x = int(x)
    y = int(y)
    if d == "L":
        um[1] = max(um[1],y)
        dm[1] = min(dm[1],y)
        lm[2] = min(lm[2],x)
        rm[0] = max(rm[0],x)
    if d == "R":
        um[1] = max(um[1],y)
        dm[1] = min(dm[1],y)
        lm[0] = min(lm[0],x)
        rm[2] = max(rm[2],x)
    if d == "U":
        um[2] = max(um[2],y)
        dm[0] = min(dm[0],y)
        lm[1] = min(lm[1],x)
        rm[1] = max(rm[1],x)
    if d == "D":
        um[0] = max(um[0],y)
        dm[2] = min(dm[2],y)
        lm[1] = min(lm[1],x)
        rm[1] = max(rm[1],x)

time = [0]

def calc(t):
    x = max(rm[1],rm[0]-t,rm[2]+t) -min(lm[1],lm[0]+t,lm[2]-t)
    y = max(um[1],um[0]-t,um[2]+t) -min(dm[1],dm[0]+t,dm[2]-t)
    return x*y

for i in range(3):
    for j in range(i):
        t = (lm[i]-lm[j])/(i-j)
        if t > 0:
            time.append(t)
        t = (dm[i]-dm[j])/(i-j)
        if t > 0:
            time.append(t)
        t = (rm[j]-rm[i])/(i-j)
        if t > 0:
            time.append(t)
        t = (um[j]-um[i])/(i-j)
        if t > 0:
            time.append(t)

ans = float("INF")
for t in time:
    ans = min(ans,calc(t))
print(ans)