Minimum Bounding Box

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

inputFormat

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

outputFormat

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

样例

2
0 3 D
3 0 L

0