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')
N = int(input())
d = {'R':[[],[]],'L':[[],[]],'U':[[],[]],'D':[[],[]]}
for i in range(N):
    x,y,f = input().split()
    x = int(x)
    y = int(y)
    d[f][0].append(x)
    d[f][1].append(y)

Ts = []

xM = max(max(d['U'][0]+[-INF]),max(d['D'][0]+[-INF]))
xMr = max(d['R'][0]+[-INF])
xMl = max(d['L'][0]+[-INF])

def xmax(T):
    return max(xM,xMr+T,xMl-T)

Ts += [max(0,xMl-xM),max(0,xM-xMr),max(0,(xMl-xMr)/2)]

xm = min(min(d['U'][0]+[INF]),min(d['D'][0]+[INF]))
xmr = min(d['R'][0]+[INF])
xml = min(d['L'][0]+[INF])

def xmin(T):
    return min(xm,xmr+T,xml-T)

Ts += [max(0,xml-xm),max(0,xm-xmr),max(0,(xml-xmr)/2)]

yM = max(max(d['R'][1]+[-INF]),max(d['L'][1]+[-INF]))
yMu = max(d['U'][1]+[-INF])
yMd = max(d['D'][1]+[-INF])

def ymax(T):
    return max(yM,yMu+T,yMd-T)

Ts += [max(0,yMd-yM),max(0,yM-yMu),max(0,(yMd-yMu)/2)]

ym = min(min(d['R'][1]+[INF]),min(d['L'][1]+[INF]))
ymu = min(d['U'][1]+[INF])
ymd = min(d['D'][1]+[INF])

def ymin(T):
    return min(ym,ymu+T,ymd-T)

Ts += [max(0,ymd-ym),max(0,ym-ymu),max(0,(ymd-ymu)/2)]

ans = INF

for T in Ts:
    ans = min(ans,(xmax(T)-xmin(T))*(ymax(T)-ymin(T)))

print(ans)