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 main():
    R_edge, L_edge, U_edge, D_edge = [None]*3, [None]*3, [None]*3, [None]*3
    n = int(input())
    xyd = [input().split() for _ in [0]*n]
    xyd = [(int(x), int(y), d) for x, y, d in xyd]
    for x, y, d in xyd:
        if d in ["R", "L"]:
            if U_edge[1] is None:
                U_edge[1] = y
            else:
                U_edge[1] = max(U_edge[1], y)
            if D_edge[1] is None:
                D_edge[1] = y
            else:
                D_edge[1] = min(D_edge[1], y)
        else:
            if R_edge[1] is None:
                R_edge[1] = x
            else:
                R_edge[1] = max(R_edge[1], x)
            if L_edge[1] is None:
                L_edge[1] = x
            else:
                L_edge[1] = min(L_edge[1], x)
        for p, q, r in [[R_edge, "R", x], [L_edge, "L", x], [U_edge, "U", y], [D_edge, "D", y]]:
            if d == q:
                if p[0] is None:
                    p[0] = r
                    p[2] = r
                else:
                    p[0] = min(p[0], r)
                    p[2] = max(p[2], r)

    def area(t):
        RL, UD = [], []
        if R_edge[0] is not None:
            RL += [t+R_edge[0], t+R_edge[2]]
        if R_edge[1] is not None:
            RL += [R_edge[1]]
        if L_edge[0] is not None:
            RL += [-t+L_edge[0], -t+L_edge[2]]
        if L_edge[1] is not None:
            RL += [L_edge[1]]
        if U_edge[0] is not None:
            UD += [t+U_edge[0], t+U_edge[2]]
        if U_edge[1] is not None:
            UD += [U_edge[1]]
        if D_edge[0] is not None:
            UD += [-t+D_edge[0], -t+D_edge[2]]
        if D_edge[1] is not None:
            UD += [D_edge[1]]
        if len(RL)*len(UD) == 0:
            return 0
        else:
            return (max(RL)-min(RL))*(max(UD)-min(UD))

    t = [0]
    for edge in [R_edge, L_edge, U_edge, D_edge]:
        if None not in edge:
            t.append(abs(edge[1]-edge[0]))
            t.append(abs(edge[1]-edge[2]))
    for edge1, edge2 in [[R_edge, L_edge], [U_edge, D_edge]]:
        if None not in [edge1[1], edge2[0]]:
            t.append(abs(edge1[1]-edge2[0]))
            t.append(abs(edge1[1]-edge2[2]))
        if None not in [edge2[1], edge1[0]]:
            t.append(abs(edge2[1]-edge1[0]))
            t.append(abs(edge2[1]-edge1[2]))
        if None not in [edge1[0], edge2[0]]:
            for i in [0, 2]:
                for j in [0, 2]:
                    t.append(abs(edge2[i]-edge1[j])/2)

    print(min([area(i) for i in t]))


main()