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())

xConstMin, xConstMax = INF, -INF
xAscMin, xAscMax = INF, -INF
xDescMin, xDescMax = INF, -INF
yConstMin, yConstMax = INF, -INF
yAscMin, yAscMax = INF, -INF
yDescMin, yDescMax = INF, -INF
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    if d == 'R':
        xAscMax = max(xAscMax, x)
        xAscMin = min(xAscMin, x)
        yConstMax = max(yConstMax, y)
        yConstMin = min(yConstMin, y)
    elif d == 'L':
        xDescMax = max(xDescMax, x)
        xDescMin = min(xDescMin, x)
        yConstMax = max(yConstMax, y)
        yConstMin = min(yConstMin, y)
    elif d == 'U':
        xConstMax = max(xConstMax, x)
        xConstMin = min(xConstMin, x)
        yAscMax = max(yAscMax, y)
        yAscMin = min(yAscMin, y)
    elif d == 'D':
        xConstMax = max(xConstMax, x)
        xConstMin = min(xConstMin, x)
        yDescMax = max(yDescMax, y)
        yDescMin = min(yDescMin, y)

tms = []

t1 = max(0, xDescMax - xConstMax)
t2 = max(0, xConstMax - xAscMax)
if t1 >= t2:
    t = max(0, (xDescMax-xAscMax)/2)
    tms.append(t)
else:
    tms.append(t1)
    tms.append(t2)

t1 = max(0, xConstMin - xAscMin)
t2 = max(0, xDescMin - xConstMin)
if t1 >= t2:
    t = max(0, (xDescMin-xAscMin)/2)
    tms.append(t)
else:
    tms.append(t1)
    tms.append(t2)

t1 = max(0, yDescMax - yConstMax)
t2 = max(0, yConstMax - yAscMax)
if t1 >= t2:
    t = max(0, (yDescMax-yAscMax)/2)
    tms.append(t)
else:
    tms.append(t1)
    tms.append(t2)

t1 = max(0, yConstMin - yAscMin)
t2 = max(0, yDescMin - yConstMin)
if t1 >= t2:
    t = max(0, (yDescMin-yAscMin)/2)
    tms.append(t)
else:
    tms.append(t1)
    tms.append(t2)

ans = INF
for tm in tms:
    if tm == INF: continue

    xs = [xConstMin, xConstMax, xAscMin+tm, xAscMax+tm, xDescMin-tm, xDescMax-tm]
    ys = [yConstMin, yConstMax, yAscMin+tm, yAscMax+tm, yDescMin-tm, yDescMax-tm]

    xMin, xMax = INF, -INF
    for x in xs:
        if x == INF or x == -INF: continue
        xMin = min(xMin, x)
        xMax = max(xMax, x)

    yMin, yMax = INF, -INF
    for y in ys:
        if y == INF or y == -INF: continue
        yMin = min(yMin, y)
        yMax = max(yMax, y)

    ans = min(ans, (xMax-xMin)*(yMax-yMin))

print(ans)