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 itertools import combinations
input = sys.stdin.readline
n = int(input())

xl = []
xr = []
xc = []
yt = []
yb = []
yc = []
for i in range(n):
    x,y,d = input().split()
    x,y = int(x), int(y)
    if d == "R":
        xr.append(x)
        yc.append(y)
    elif d == "L":
        xl.append(x)
        yc.append(y)
    elif d == "U":
        xc.append(x)
        yt.append(y)
    else:
        xc.append(x)
        yb.append(y)
xr.sort()
xl.sort()
xc.sort()
yt.sort()
yb.sort()
yc.sort()

# xの最小値
xr_min = xr[0] if xr else None
xl_min = xl[0] if xl else None
xc_min = xc[0] if xc else None
xmin = [xr_min, xl_min, xc_min]

# xの最大値 最小化
xr_max = xr[-1] if xr else None
xl_max = xl[-1] if xl else None
xc_max = xc[-1] if xc else None
xmax = [xr_max, xl_max, xc_max]

# 上に行く　最小化
yt_max = yt[-1] if yt else None
yb_max = yb[-1] if yb else None
yc_max = yc[-1] if yc else None
ymax = [yt_max, yb_max, yc_max]

# 下に行く
yt_min = yt[0] if yt else None
yb_min = yb[0] if yb else None
yc_min = yc[0] if yc else None
ymin = [yt_min, yb_min, yc_min]

def cross(p1, p2):
    ret = []
    if p1 is None or p2 is None:
        return ret
    sub = abs(p1-p2)
    ret.append(sub)
    ret.append(sub/2)
    ret.append(sub/2+1)
    return ret

def check(t, xmax, xmin, ymax, ymin):
    op = [+1, -1, 0]
    xmax_ = -float("inf")
    xmin_ = float("inf")
    ymax_ = -float("inf")
    ymin_ = float("inf")
    # xmax
    for i, x in enumerate(xmax):
        if x is not None:
            xmax_ = max(xmax_, x+t*op[i])
    # xmin
    for i, x in enumerate(xmin):
        if x is not None:
            xmin_ = min(xmin_, x+t*op[i])
    # ymax
    for i, y in enumerate(ymax):
        if y is not None:
            ymax_ = max(ymax_, y+t*op[i])
    # ymin
    for i, y in enumerate(ymin):
        if y is not None:
            ymin_ = min(ymin_, y+t*op[i])
    return (xmax_-xmin_)*(ymax_-ymin_)

time_candidate = [0]

for lis in [xmin, xmax, ymin, ymax]:
    for p1, p2 in combinations(lis, 2):
        time_candidate.extend(cross(p1,p2))

ans = float("inf")
for i in set(time_candidate):
    ans_tmp = check(i, xmax, xmin, ymax, ymin)
    ans = min(ans, check(i, xmax, xmin, ymax, ymin))
print(ans)