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:
INF = float('inf')
from collections import defaultdict
N = int(input())
dx = defaultdict(list)
dy = defaultdict(list)
for i in range(N):
    x,y,d = input().split()
    x = int(x)
    y = int(y)
    dx[d].append(x)
    dy[d].append(y)

mxl = INF
if 'L' in dx:
    mxl = min(dx['L'])
mxr = INF
if 'R' in dx:
    mxr = min(dx['R'])
mxud = INF
if 'U' in dx:
    mxud = min(dx['U'])
if 'D' in dx:
    mxud = min(min(dx['D']),mxud)
Mxl = -INF
if 'L' in dx:
    Mxl = max(dx['L'])
Mxr = -INF
if 'R' in dx:
    Mxr = max(dx['R'])
Mxud = -INF
if 'U' in dx:
    Mxud = max(dx['U'])
if 'D' in dx:
    Mxud = max(max(dx['D']),Mxud)
myu = INF
if 'U' in dy:
    myu = min(dy['U'])
myd = INF
if 'D' in dy:
    myd = min(dy['D'])
mylr = INF
if 'L' in dy:
    mylr = min(dy['L'])
if 'R' in dy:
    mylr = min(min(dy['R']),mylr)
Myu = -INF
if 'U' in dy:
    Myu = max(dy['U'])
Myd = -INF
if 'D' in dy:
    Myd = max(dy['D'])
Mylr = -INF
if 'L' in dy:
    Mylr = max(dy['L'])
if 'R' in dy:
    Mylr = max(max(dy['R']),Mylr)

def xmin(t):
    return min(mxl-t,mxr+t,mxud)

def xmax(t):
    return max(Mxl-t,Mxr+t,Mxud)

def ymin(t):
    return min(myu+t,myd-t,mylr)

def ymax(t):
    return max(Myu+t,Myd-t,Mylr)

cand = [0,(mxl-mxr)/2,mxl-mxud,mxud-mxr,(Mxl-Mxr)/2,Mxl-Mxud,Mxud-Mxr,(myd-myu)/2,mylr-myu,myd-mylr,(Myd-Myu)/2,Mylr-Myu,Myd-Mylr]

ans = INF
for t in cand:
    if t < 0:
        continue
    ans = min(ans,(xmax(t)-xmin(t))*(ymax(t)-ymin(t)))
print(ans)