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():
    import sys
    input = sys.stdin.readline

    N = int(input())
    inf = 2 * 10**9
    L = [inf, inf, inf]
    R = [-inf, -inf, -inf]
    U = [-inf, -inf, -inf]
    D = [inf, inf, inf]
    for _ in range(N):
        x, y, d = input().split()
        x = int(x) * 2
        y = int(y) * 2
        if d == 'L':
            L[0] = min(L[0], x)
            R[1] = max(R[1], x)
            U[2] = max(U[2], y)
            D[2] = min(D[2], y)
        elif d == 'R':
            L[1] = min(L[1], x)
            R[0] = max(R[0], x)
            U[2] = max(U[2], y)
            D[2] = min(D[2], y)
        elif d == 'U':
            L[2] = min(L[2], x)
            R[2] = max(R[2], x)
            U[0] = max(U[0], y)
            D[1] = min(D[1], y)
        else:
            L[2] = min(L[2], x)
            R[2] = max(R[2], x)
            U[1] = max(U[1], y)
            D[0] = min(D[0], y)

    def calc(t):
        if t < 0:
            return 10**20
        xmin = min(L[0] - t, L[1] + t, L[2])
        xmax = max(R[0] + t, R[1] - t, R[2])
        ymax = max(U[0] + t, U[1] - t, U[2])
        ymin = min(D[0] - t, D[1] + t, D[2])
        return (xmax - xmin) * (ymax - ymin)

    ans = calc(0)
    ans = min(ans, calc((L[0] - L[1]) // 2), calc(L[0] - L[2]), calc(L[2] - L[1]))
    ans = min(ans, calc((R[1] - R[0]) // 2), calc(R[2] - R[0]), calc(R[1] - R[2]))
    ans = min(ans, calc((U[1] - U[0]) // 2), calc(U[2] - U[0]), calc(U[1] - U[2]))
    ans = min(ans, calc((D[0] - D[1]) // 2), calc(D[0] - D[2]), calc(D[2] - D[1]))
    print(ans / 4)


if __name__ == '__main__':
    main()