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:
n = int(input())
m = {}
for _ in range(n):
    x, y, d = input().split()
    x, y = int(x) * 2, int(y) * 2
    if d not in m:
        m[d] = [1000000000, -1000000000, 1000000000, -1000000000]
    m[d][0] = min(m[d][0], x)
    m[d][1] = max(m[d][1], x)
    m[d][2] = min(m[d][2], y)
    m[d][3] = max(m[d][3], y)

dx = {'L': -1, 'R': 1, 'U': 0, 'D': 0}
dy = {'L': 0, 'R': 0, 'U': 1, 'D': -1}

px = []
py = []
for d in 'LRUD':
    if d in m:
        px.append((m[d][0], dx[d]))
        px.append((m[d][1], dx[d]))
        py.append((m[d][2], dy[d]))
        py.append((m[d][3], dy[d]))

times = [0]
def append(pa, pb):
    (a, da) = pa
    (b, db) = pb
    if db != da:
        t = (a - b) // (db - da)
        if t >= 0:
            times.append(t)

for i in range(len(px)):
    for j in range(i + 1, len(px)):
        append(px[i], px[j])

for i in range(len(py)):
    for j in range(i + 1, len(py)):
        append(py[i], py[j])

ret = 1000000000000000000
for t in times:
    bb = [1000000000, -1000000000, 1000000000, -1000000000]
    for d in 'LRUD':
        if d in m:
            bb[0] = min(bb[0], m[d][0] + dx[d] * t)
            bb[1] = max(bb[1], m[d][1] + dx[d] * t)
            bb[2] = min(bb[2], m[d][2] + dy[d] * t)
            bb[3] = max(bb[3], m[d][3] + dy[d] * t)
    ret = min(ret, (bb[1] - bb[0]) * (bb[3] - bb[2]))

print(ret / 4.0)