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:
def analyze(points, left_static, right_static):
    """
    (x0, +1 or -1) in points
    """

    rightest_neg = -10**9
    leftest_neg = 10**9
    rightest_pos = -10**9
    leftest_pos = 10**9
    for x, d in points:
        if d == 1:
            rightest_pos = max(rightest_pos, x)
            leftest_pos = min(leftest_pos, x)
        else:
            rightest_neg = max(rightest_neg, x)
            leftest_neg = min(leftest_neg, x)


    max_t1 = rightest_neg - right_static
    max_t2 = right_static - rightest_pos
    if max_t1 > max_t2:
        max_t1 = max_t2 = (rightest_neg-rightest_pos)/2
    max_t1 = max(0, max_t1)
    max_t2 = max(0, max_t2)
    max_x0 = max(rightest_pos, rightest_neg, right_static)
    max_x1 = max(rightest_pos + max_t1, rightest_neg - max_t1, right_static)
    def get_xmax(t):
        if t > max_t2:
            return max_x1 + t-max_t2
        elif t > max_t1:
            return max_x1
        else:
            return max_x0 - t

    min_t1 = left_static - leftest_pos
    min_t2 = leftest_neg - left_static
    if min_t1 > min_t2:
        min_t1 = min_t2 = (leftest_neg - leftest_pos)/2
    min_t1 = max(0, min_t1)
    min_t2 = max(0, min_t2)
    min_x0 = min(leftest_pos, leftest_neg, left_static)
    min_x1 = min(leftest_pos + min_t1, leftest_neg - min_t1, left_static)

    def get_xmin(t):
        if t > min_t2:
            return min_x1 - t + min_t2
        elif t > min_t1:
            return min_x1
        else:
            return min_x0 + t

    T = sorted((max_t1, max_t2, min_t1, min_t2))
    D = [get_xmax(t)-get_xmin(t) for t in T]
    return T,D



N = int(input())

conv = {'R':0,'U':1,'L':2,'D':3}
points = [(lambda i: (int(i[0]), int(i[1]), conv[i[2]]))(input().split()) for _ in range(N)]


xt, xd = analyze([(x, 1 if d == 0 else -1) for x,y,d in points if d%2==0],
                    min((x for x,y,d in points if d%2==1), default=10**9),
                    max((x for x,y,d in points if d%2==1), default=-10**9))

yt, yd = analyze([(y, 1 if d == 1 else -1) for x,y,d in points if d%2==1],
                    min((y for x,y,d in points if d%2==0), default=10**9),
                    max((y for x,y,d in points if d%2==0), default=-10**9))

def get_w(t):
    a,b,c,d = xt

    if t < a:
        return -2, xd[0] + 2*a
    elif t < b:
        return -1, xd[0] + a
    elif t < c:
        return 0, xd[1]
    elif t < d:
        return 1, xd[2] - c
    else:
        return 2, xd[3] - 2*d

def get_h(t):
    a,b,c,d = yt

    if t < a:
        return -2, yd[0] + 2*a
    elif t < b:
        return -1, yd[0] + a
    elif t < c:
        return 0, yd[1]
    elif t < d:
        return 1, yd[2] - c
    else:
        return 2, yd[3] - 2*d

T = sorted(xt+yt)

def it():
    ne = iter(T)
    next(ne)
    for a,b in zip(T,ne):
        t = (a+b)/2

        wa, wb = get_w(t)
        ha, hb = get_h(t)
        if wa*ha > 0 and a < -(wb*ha+wa*hb)/(2*wa*ha) < b:
            t = -(wb*ha+wa*hb)/(2*wa*ha)
            yield ((wa*t+wb)*(ha*t+hb), t)
        else:
            yield ((wa*a+wb)*(ha*a+hb), a)
            yield ((wa*b+wb)*(ha*b+hb), b)

print(min(it())[0])