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:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 998244353
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(): return [list(map(int, l.split())) for l in sys.stdin.readlines()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def pe(s): return print(str(s), file=sys.stderr)
def JA(a, sep): return sep.join(map(str, a))
def JAA(a, s, t): return s.join(t.join(map(str, b)) for b in a)


def main():
    n = I()
    aa = [LS() for _ in range(n)]
    xi = collections.defaultdict(lambda: inf)
    xa = collections.defaultdict(lambda: -inf)
    yi = collections.defaultdict(lambda: inf)
    ya = collections.defaultdict(lambda: -inf)
    km = 0
    for x,y,d in aa:
        x = int(x)
        y = int(y)
        if km < abs(x):
            km = abs(x)
        if km < abs(y):
            km = abs(y)
        if xi[d] > x:
            xi[d] = x
        if xa[d] < x:
            xa[d] = x
        if yi[d] > y:
            yi[d] = y
        if ya[d] < y:
            ya[d] = y

    ts = set([0])

    for d in [xi,xa,yi,ya]:
        ks = list(d.keys())
        for k in ks:
            for e in ks:
                ts.add(abs(d[k] - d[e]))
                ts.add(abs(d[k] - d[e]) / 2)

    def f(i):
        xxi = inf
        xxa = -inf
        yyi = inf
        yya = -inf
        for d,x in xi.items():
            if d == 'L':
                x -= i
            elif d == 'R':
                x += i
            if xxi > x:
                xxi = x
        for d,x in xa.items():
            if d == 'L':
                x -= i
            elif d == 'R':
                x += i
            if xxa < x:
                xxa = x
        for d,y in yi.items():
            if d == 'D':
                y -= i
            elif d == 'U':
                y += i
            if yyi > y:
                yyi = y
        for d,y in ya.items():
            if d == 'D':
                y -= i
            elif d == 'U':
                y += i
            if yya < y:
                yya = y

        return (xxa-xxi) * (yya-yyi)

    r = f(0)
    for i in ts:
        t = f(i)
        if r > t:
            r = t

    return '{:0.3f}'.format(r)


print(main())