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:
#!/usr/bin/env python3
import sys

inf = float('inf')

def solve(N: int, x: "List[int]", y: "List[int]", d: "List[str]"):
    D_xmin = [inf for dd in [-1, 0, 1]]
    D_xmax = [-inf for dd in [-1, 0, 1]]
    D_ymin = [inf for dd in [-1, 0, 1]]
    D_ymax = [-inf for dd in [-1, 0, 1]]
    trans_x = {'U': 1, 'D': 1, 'L': 0, 'R': 2}
    trans_y = {'U': 2, 'D': 0, 'L': 1, 'R': 1}
    
    for xx, yy, dd in zip(x, y, d):
        D_xmin[trans_x[dd]] = min(D_xmin[trans_x[dd]], xx)
        D_xmax[trans_x[dd]] = max(D_xmax[trans_x[dd]], xx)
        D_ymin[trans_y[dd]] = min(D_ymin[trans_y[dd]], yy)
        D_ymax[trans_y[dd]] = max(D_ymax[trans_y[dd]], yy)
    
    ts = [0]
    for D in [D_xmin, D_xmax, D_ymin, D_ymax]:
        ts.append(D[0] - D[1])
        ts.append(D[1] - D[2])
        ts.append((D[0] - D[2]) / 2)

    res = inf
    for t in ts:
        if t < 0:
            continue
        xmin = min(D_xmin[0] - t, D_xmin[1], D_xmin[2] + t)
        xmax = max(D_xmax[0] - t, D_xmax[1], D_xmax[2] + t)
        ymin = min(D_ymin[0] - t, D_ymin[1], D_ymin[2] + t)
        ymax = max(D_ymax[0] - t, D_ymax[1], D_ymax[2] + t)
        res = min(res, (xmax - xmin) * (ymax - ymin))

    print(res)
    return


# Generated by 1.1.4 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    x = [int()] * (N)  # type: "List[int]" 
    y = [int()] * (N)  # type: "List[int]" 
    d = [str()] * (N)  # type: "List[str]" 
    for i in range(N):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
        d[i] = next(tokens)
    solve(N, x, y, d)

if __name__ == '__main__':
    main()