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:
from decimal import *
getcontext().prec = 100
N = int(input())
Xmi, Xma, Ymi, Yma, DYmi, DYma, UYmi, UYma, RXmi, RXma, LXmi, LXma = [(10**10), -(10**10)] * 6
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    
    if d == "R":
        RXmi = min(RXmi, x)
        RXma = max(RXma, x)
    elif d == "L":
        LXmi = min(LXmi, x)
        LXma = max(LXma, x)
    else:
        Xmi = min(Xmi, x)
        Xma = max(Xma, x)
        
    if d == "U":
        UYmi = min(UYmi, y)
        UYma = max(UYma, y)
    elif d == "D":
        DYmi = min(DYmi, y)
        DYma = max(DYma, y)
    else:
        Ymi = min(Ymi, y)
        Yma = max(Yma, y)

def calc(t):
    xmi = min(RXmi+t, LXmi-t, Xmi)
    xma = max(RXma+t, LXma-t, Xma)
    ymi = min(UYmi+t, DYmi-t, Ymi)
    yma = max(UYma+t, DYma-t, Yma)
    return max(yma-ymi, 0)*max(xma-xmi, 0)
    
def dii(t):
    a = Decimal("0.00000001")
    return calc(t+a) - calc(t-a)

l = Decimal("0")
r = Decimal("10000000000")
for _ in range(500):
    m = (l+r)/2
    if dii(m) > 0:
        r = m
    else:
        l = m
print(calc(m))