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 f_minimum_bounding_box(N, Positions, INF=float('inf')):
    # 参考: https://betrue12.hateblo.jp/entry/2019/06/17/202327
    X, Y = [{'L': [], 'R': [], 'U': [], 'D': []} for _ in range(2)]
    for x, y, d in Positions:
        X[d].append(int(x) * 2)
        Y[d].append(int(y) * 2)

    xs, ys = [], []
    for c in 'LRUD':
        if len(X[c]) != 0:
            xs.extend((max(X[c]), min(X[c])))
        if len(Y[c]) != 0:
            ys.extend((max(Y[c]), min(Y[c])))

    cand = []
    for x1 in xs:
        for x2 in xs:
            d = abs(x1 - x2)
            cand.extend((d, d // 2))
    for y1 in ys:
        for y2 in ys:
            d = abs(y1 - y2)
            cand.extend((d, d // 2))

    dx = {'L': -1, 'R': 1, 'U': 0, 'D': 0}
    dy = {'L': 0, 'R': 0, 'U': 1, 'D': -1}
    ans = INF
    for d in cand:
        xmax, ymax, xmin, ymin = -INF, -INF, INF, INF
        for c in 'LRUD':
            for i in range(len(X[c])):
                x = X[c][i] + dx[c] * d
                xmax = max(xmax, x)
                xmin = min(xmin, x)
            for j in range(len(Y[c])):
                y = Y[c][j] + dy[c] * d
                ymax = max(ymax, y)
                ymin = min(ymin, y)
        tmp = (xmax - xmin) * (ymax - ymin)
        ans = min(ans, tmp)
    return round(ans / 4, 12)

N = int(input())
Positions = [[i for i in input().split()] for j in range(N)]
print(f_minimum_bounding_box(N, Positions))