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

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见题面