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:
N=int(input())
import sys
input=sys.stdin.readline
inf=10**20
dd = {
        'R':[-inf]*3,
        'L':[inf]*3,
        'U':[-inf]*3,
        'D':[inf]*3,
        }
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    if d == 'R':
        dd['R'][0] = max(x, dd['R'][0])
        dd['L'][1] = min(x, dd['L'][1])
        dd['U'][2] = max(y, dd['U'][2])
        dd['D'][2] = min(y, dd['D'][2])
    elif d == 'L':
        dd['L'][0] = min(x, dd['L'][0])
        dd['R'][1] = max(x, dd['R'][1])
        dd['U'][2] = max(y, dd['U'][2])
        dd['D'][2] = min(y, dd['D'][2])
    elif d == 'U':
        dd['R'][2] = max(x, dd['R'][2])
        dd['L'][2] = min(x, dd['L'][2])
        dd['U'][0] = max(y, dd['U'][0])
        dd['D'][1] = min(y, dd['D'][1])
    elif d == 'D':
        dd['R'][2] = max(x, dd['R'][2])
        dd['L'][2] = min(x, dd['L'][2])
        dd['U'][1] = max(y, dd['U'][1])
        dd['D'][0] = min(y, dd['D'][0])

tls = []
for d in "RLUD":
    m = -1 if d in 'RU' else 1
    t1 = -m*(dd[d][1] - dd[d][2])
    t2 = -m*(dd[d][2] - dd[d][0])
    t3 = m*float(dd[d][0] - dd[d][1])/2
    #print(d, m, t1,t2,t3)
    if t1 < t3 and t3 < t2:
        if t1 > 0:
            tls.append((0, m, dd[d][1], d))
        if t2 > 0:
            tls.append((max(0, t1), 0, dd[d][2], d))
        tls.append((max(0, t2), -m, dd[d][0], d))
    else:
        if t3 > 0:
            tls.append((0, m, dd[d][1], d))
        tls.append((max(0, t3), -m, dd[d][0], d))

tls.sort()
btl = 0
r = 10**20
for t, a, b, d in tls:
    if btl > 10**10:
        btl = inf
        break
    if t != btl:
        a1=(dd['R'][0] - dd['L'][0])
        a2=(dd['U'][0] - dd['D'][0])
        b1=(dd['R'][1] - dd['L'][1])
        b2=(dd['U'][1] - dd['D'][1])
        r = min(r, (a1*t+b1)*(a2*t+b2))
        r = min(r, (a1*btl+b1)*(a2*btl+b2))
        #print(t, btl, dd['R'], dd['L'], dd['U'], dd['D'], r)
    dd[d] = (a, b)
    btl = t
if btl < inf:
    t = inf
    a1=(dd['R'][0] - dd['L'][0])
    a2=(dd['U'][0] - dd['D'][0])
    b1=(dd['R'][1] - dd['L'][1])
    b2=(dd['U'][1] - dd['D'][1])
    r = min(r, (a1*t+b1)*(a2*t+b2))
    r = min(r, (a1*btl+b1)*(a2*btl+b2))
#print(t, btl, dd['R'], dd['L'], dd['U'], dd['D'])

print(r)
#print(tls)