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

from math import floor


def check(t):
    maxx, minx, maxy, miny = ud_maxx, ud_minx, lr_maxy, lr_miny
    for x, y in dots['R']:
        maxx = max(maxx, x + t)
        minx = min(minx, x + t)
    for x, y in dots['L']:
        maxx = max(maxx, x - t)
        minx = min(minx, x - t)
    for x, y in dots['U']:
        maxy = max(maxy, y + t)
        miny = min(miny, y + t)
    for x, y in dots['D']:
        maxy = max(maxy, y - t)
        miny = min(miny, y - t)
    return (maxx - minx) * (maxy - miny)


n = int(input())
dots = {'R': set(), 'L': set(), 'U': set(), 'D': set()}
lr_maxy, lr_miny, ud_maxx, ud_minx = -1e9, 1e9, -1e9, 1e9
for line in sys.stdin:
    x, y, d = line.rstrip().split()
    x, y = int(x), int(y)
    dots[d].add((x, y))
    if d in 'LR':
        lr_maxy = max(lr_maxy, y)
        lr_miny = min(lr_miny, y)
    else:
        ud_maxx = max(ud_maxx, x)
        ud_minx = min(ud_minx, x)

l = 0.0
r = float(1 << 30)

while l < r - 1:
    m1 = l + floor((r - l) / 3 * 2) / 2
    m2 = l + floor((r - l) / 3 * 4) / 2
    c1 = check(m1)
    c2 = check(m2)
    # print(l, r, m1, m2, c1, c2)
    if c1 >= c2:
        l = m1
    else:
        r = m2

ans = float(1e17)
l = max(0.0, floor(l * 2 - 16) / 2)
while l <= r + 8:
    ans = min(ans, check(l))
    l += 0.5
print(ans)