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:
inf = float("inf")
N = int(input())
if N==1:
    print(0)
    exit()
lr = inf
ll = inf
rr = -inf
rl = -inf
ud = -inf
uu = -inf
dd = inf
du = inf
l_stop = inf
r_stop = -inf
u_stop = -inf
d_stop = inf
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    if d=="R":
        lr = min(lr, x)
        rr = max(rr, x)
    elif d=="L":
        rl = max(rl, x)
        ll = min(ll, x)
    elif d=="U":
        du = min(du, y)
        uu = max(uu, y)
    else:
        ud = max(ud, y)
        dd = min(dd, y)
    if d=="R" or d=="L":
        u_stop = max(u_stop, y)
        d_stop = min(d_stop, y)
    else:
        l_stop = min(l_stop, x)
        r_stop = max(r_stop, x)


def f(t):
    r = max(r_stop, rr+t, rl-t)
    l = min(l_stop, ll-t, lr+t)
    u = max(u_stop, uu+t, ud-t)
    d = min(d_stop, dd-t, du+t)
    return (r-l) * (u-d)
#print(f(1))

high = 10**8
high = float(high)
low = 0.0
while high - low > 0.000001:
    #print(high, low)
    mid_left = high/3+low*2/3
    mid_right = high*2/3+low/3
    if f(mid_left) >= f(mid_right):
        low = mid_left
    else:
        high = mid_right
print(f(round(high, 3)))