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())

PS = [[], [], [], []]
S = "RLUD".index

for i in range(N):
    x, y, d = input().split(); x = int(x); y = int(y)
    PS[S(d)].append((x, y))

T = [0]
INF = 10**9

dymin = INF; dymax = -INF
P = []
for i in [0, 1]:
    xmin = INF; xmax = -INF
    for x, y in PS[i]:
        dymin = min(dymin, y)
        dymax = max(dymax, y)
        xmin = min(xmin, x)
        xmax = max(xmax, x)
    P.append((xmin, xmax))
for x0 in P[0]:
    for x1 in P[1]:
        T.append(max(x1 - x0, 0) / 2.)

dxmin = INF; dxmax = -INF
Q = []
for i in [2, 3]:
    ymin = INF; ymax = -INF
    for x, y in PS[i]:
        dxmin = min(dxmin, x)
        dxmax = max(dxmax, x)
        ymin = min(ymin, y)
        ymax = max(ymax, y)
    Q.append((ymin, ymax))
for y0 in Q[0]:
    for y1 in Q[1]:
        T.append(max(y1 - y0, 0) / 2.)

for x0 in [dxmin, dxmax]:
    for x in P[0]:
        T.append(max(x0 - x, 0))
    for x in P[1]:
        T.append(max(x - x0, 0))
for y0 in [dymin, dymax]:
    for y in Q[0]:
        T.append(max(y0 - y, 0))
    for y in Q[1]:
        T.append(max(y - y0, 0))

ans = 10**30
for t in T:
    xmin = dxmin; xmax = dxmax
    ymin = dymin; ymax = dymax

    xi, xa = P[0]
    if xi != INF:
        xmin = min(xmin, xi+t)
        xmax = max(xmax, xa+t)
    xi, xa = P[1]
    if xi != INF:
        xmin = min(xmin, xi-t)
        xmax = max(xmax, xa-t)
    yi, ya = Q[0]
    if yi != INF:
        ymin = min(ymin, yi+t)
        ymax = max(ymax, ya+t)
    yi, ya = Q[1]
    if yi != INF:
        ymin = min(ymin, yi-t)
        ymax = max(ymax, ya-t)
    ans = min(ans, (xmax - xmin) * (ymax - ymin))
print("%.10f" % ans)