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
sys.setrecursionlimit(10**7)
INF = 10 ** 9
MOD = 10 ** 9 + 7
def YesNo(x): return 'Yes' if x else 'No'
def LI(): return [int(x) for x in sys.stdin.readline().split()]
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 II(): return int(sys.stdin.readline())
def SI(): return input()

def main():
    N = II()
    xp9, xm9, xf9, yp9, ym9, yf9 = [-INF] * 6
    xp0, xm0, xf0, yp0, ym0, yf0 = [INF] * 6
    for _ in range(N):
        x, y, d = LS()
        x = int(x)
        y = int(y)
        if d == 'R':
            xp9 = max(xp9, x)
            xp0 = min(xp0, x)
            yf9 = max(yf9, y)
            yf0 = min(yf0, y)
        elif d == 'L':
            xm9 = max(xm9, x)
            xm0 = min(xm0, x)
            yf9 = max(yf9, y)
            yf0 = min(yf0, y)
        elif d == 'U':
            xf9 = max(xf9, x)
            xf0 = min(xf0, x)
            yp9 = max(yp9, y)
            yp0 = min(yp0, y)
        elif d == 'D':
            xf9 = max(xf9, x)
            xf0 = min(xf0, x)
            ym9 = max(ym9, y)
            ym0 = min(ym0, y)
    ts = [0]
    ts += [xf0 - xp0, xf9 - xp0, xf0 - xp9, xf9 - xp9]
    ts += [(xm0 - xp0) * 0.5, (xm9 - xp0) * 0.5, (xm0 - xp9) * 0.5, (xm9 - xp9) * 0.5]
    ts += [xm0 - xf0, xm9 - xf0, xm0 - xf9, xm9 - xf9]
    ts += [yf0 - yp0, yf9 - yp0, yf0 - yp9, yf9 - yp9]
    ts += [(ym0 - yp0) * 0.5, (ym9 - yp0) * 0.5, (ym0 - yp9) * 0.5, (ym9 - yp9) * 0.5]
    ts += [ym0 - yf0, ym9 - yf0, ym0 - yf9, ym9 - yf9]
    ts = [t for t in ts if t >= 0]
    ans = 10 ** 18
    for t in ts:
        xmax = max(xf9, xm9 - t, xp9 + t)
        xmin = min(xf0, xm0 - t, xp0 + t)
        ymax = max(yf9, ym9 - t, yp9 + t)
        ymin = min(yf0, ym0 - t, yp0 + t)
        tmp = (xmax - xmin) * (ymax - ymin)
        ans = min(ans, tmp)

    return ans

print(main())