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 sys
N = int(input())
LU, LD, LR, LL = [], [], [], []
for _ in range(N):
    x, y, d = sys.stdin.readline().split()
    x = int(x)
    y = int(y)
    if d == 'R':
        LR.append((x, y))
    elif d == 'L':
        LL.append((x, y))
    elif d == 'U':
        LU.append((x, y))
    elif d == 'D':
        LD.append((x, y))
if LR:
    lrx, lry = map(list, zip(*LR))
else:
    lrx, lry = [], []
if LL:
    llx, lly = map(list, zip(*LL))
else:
    llx, lly = [], []
if LU:
    lux, luy = map(list, zip(*LU))
else:
    lux, luy = [], []
if LD:
    ldx, ldy = map(list, zip(*LD))
else:
    ldx, ldy = [], []

inf = 100000000000000.0
maxxp = max(lrx + [-inf])
maxxz = max(lux + ldx + [-inf])
maxxm = max(llx + [-inf])
minxp = min(lrx + [inf])
minxz = min(lux + ldx + [inf])
minxm = min(llx + [inf])

maxyp = max(luy + [-inf])
maxyz = max(lly + lry + [-inf])
maxym = max(ldy + [-inf])
minyp = min(luy + [inf])
minyz = min(lly + lry + [inf])
minym = min(ldy + [inf])

def calc(t):
    maxx = max(maxxp + t, maxxz, maxxm - t)
    minx = min(minxp + t, minxz, minxm - t)
    maxy = max(maxyp + t, maxyz, maxym - t)
    miny = min(minyp + t, minyz, minym - t)
    
    return abs(maxx - minx)*abs(maxy - miny)

lo = 0.0
hi = 10000000000.0
for _ in range(1000):
    b1 = (2*lo + hi)/3
    b2 = (lo + 2*hi)/3
    if calc(b1) < calc(b2):
        hi = b2
    else:
        lo = b1
print(calc(lo))