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:
# coding: utf-8
# Your code here!

import sys
n = int(input())

inf = float("inf")
u=d=l=r=0
umin = inf
umax = -inf
dmin = inf
dmax = -inf
lmin = inf
lmax = -inf
rmin = inf
rmax = -inf
xmin = inf
xmax = -inf
ymin = inf
ymax = -inf
xx=yy=0

for j in range(n):
    x,y,D = [i for i in input().split()]
    x=int(x); y=int(y)
    if D == "U":
        umin = min(umin,y)
        umax = max(umax,y)
        u=1
        xmin = min(xmin,x)
        xmax = max(xmax,x)
        xx=1
    if D == "D":
        dmin = min(dmin,y)
        dmax = max(dmax,y)
        d=1
        xmin = min(xmin,x)
        xmax = max(xmax,x)
        xx=1
    if D == "L":
        lmin = min(lmin,x)
        lmax = max(lmax,x)
        l=1
        ymin = min(ymin,y)
        ymax = max(ymax,y)
        yy=1
    if D == "R":
        rmin = min(rmin,x)
        rmax = max(rmax,x)
        r=1
        ymin = min(ymin,y)
        ymax = max(ymax,y)
        yy=1

def lpos(t):
    ans = inf
    if xx: ans = min(ans,xmin)
    if l: ans = min(ans,lmin-t)
    if r: ans = min(ans,rmin+t)
    return ans
def rpos(t):
    ans = -inf
    if xx: ans = max(ans,xmax)
    if l: ans = max(ans,lmax-t)
    if r: ans = max(ans,rmax+t)
    return ans

def dpos(t):
    ans = inf
    if yy: ans = min(ans,ymin)
    if u: ans = min(ans,umin+t)
    if d: ans = min(ans,dmin-t)
    return ans
def upos(t):
    ans = -inf
    if yy: ans = max(ans,ymax)
    if u: ans = max(ans,umax+t)
    if d: ans = max(ans,dmax-t)
    return ans

s = {0}
if xx and l:
    if lmin - xmin > 0: s.add(lmin - xmin)
    if lmax - xmax > 0: s.add(lmax - xmax)
if xx and r:
    if xmin - rmin > 0: s.add(xmin - rmin)
    if xmax - rmax > 0: s.add(xmax - rmax)
if l and r:
    if lmin-rmin > 0: s.add((lmin-rmin)/2)
    if lmax-rmax > 0: s.add((lmax-rmax)/2)

if yy and d:
    if dmin - ymin > 0: s.add(dmin - ymin)
    if dmax - ymax > 0: s.add(dmax - ymax)
if yy and u:
    if ymin - umin > 0: s.add(ymin - umin)
    if ymax - umax > 0: s.add(ymax - umax)
if d and u:
    if dmin-umin > 0: s.add((dmin-umin)/2)
    if dmax-umax > 0: s.add((dmax-umax)/2)
    
#print(rmax,xmax)

ans = 10**18
for t in s:
#    print(rpos(t),lpos(t),dpos(t),upos(t),xmin,ymin,xmax,ymax,xx,yy)
    area = (rpos(t)-lpos(t))*(upos(t)-dpos(t))
#    print(t,area)
    if area < ans:
        ans = area

print(ans)