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:
import sys

def main():
    input = sys.stdin.readline
    inf = 10**8 + 1
    N = int(input())
    const_x_max, right_max, left_max = -inf, -inf, -inf
    const_x_min, right_min, left_min = inf, inf, inf
    const_y_max, up_max, down_max = -inf, -inf, -inf
    const_y_min, up_min, down_min = inf, inf, inf
    for _ in range(N):
        x, y, d = map(str, input().strip().split())
        x, y = int(x), int(y)

        if d == 'R':
            right_max = max(right_max, x)
            right_min = min(right_min, x)
            const_y_max = max(const_y_max, y)
            const_y_min = min(const_y_min, y)
        elif d == 'L':
            left_max = max(left_max, x)
            left_min = min(left_min, x)
            const_y_max = max(const_y_max, y)
            const_y_min = min(const_y_min, y)
        elif d == 'U':
            const_x_max = max(const_x_max, x)
            const_x_min = min(const_x_min, x)
            up_max = max(up_max, y)
            up_min = min(up_min, y)
        else:
            const_x_max = max(const_x_max, x)
            const_x_min = min(const_x_min, x)
            down_max = max(down_max, y)
            down_min = min(down_min, y)

    inflections = set([0])
    # The time when the slope of max_x changes.
    # 1. from decrease to constant.
    inflections.add(max(0, left_max - const_x_max))
    # 2. from decrease to increase.
    inflections.add(max(0, (left_max - right_max)/2))
    # 3. from constant to increase.
    inflections.add(max(0, const_x_max - right_max))

    # The time when the slope of min_x changes.
    # 4. from increase to constatnt.
    inflections.add(max(0, const_x_min - right_min))
    # 5. from increase to decrease.
    inflections.add(max(0, (left_min - right_min)/2))
    # 6. from constant to decrease.
    inflections.add(max(0, left_min - const_x_min))

    # The time when the slope of max_y changes.
    # 7. from decrease to constant.
    inflections.add(max(0, down_max - const_y_max))
    # 8. from decrease to increase.
    inflections.add(max(0, (down_max - up_max)/2))
    # 9. from constant to increase.
    inflections.add(max(0, const_y_max - up_max))

    # The time when the slope of min_y changes.
    # 10. from increase to constatnt.
    inflections.add(max(0, const_y_min - up_min))
    # 11. from increase to decrease.
    inflections.add(max(0, (down_min - up_min)/2))
    # 12. from constant to decrease.
    inflections.add(max(0, down_min - const_y_min))


    def get_val(t):
        x0 = max(const_x_max, right_max + t, left_max - t)
        x1 = min(const_x_min, right_min + t, left_min - t)
        y0 = max(const_y_max, up_max + t, down_max - t)
        y1 = min(const_y_min, up_min + t, down_min - t)

        return (x0 - x1) * (y0 - y1)

    ans = 10**18
    for t in inflections:
        ans = min(ans, get_val(t))

    return ans


if __name__ == '__main__':
    print(main())