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
input = sys.stdin.readline

inf = 10**9

n = int(input())

if(n==1):
    print(0)
    exit()

UD_x = [inf, -1*inf]
LR_y = [inf, -1*inf]
U_y = [inf, -1*inf]
D_y = [inf, -1*inf]
R_x = [inf, -1*inf]
L_x = [inf, -1*inf]

for i in range(n):
    tmp = input().split()
    x,y = map(int, tmp[:2])
    d = tmp[2]
    if(d == 'U'):
        UD_x[0] = min(UD_x[0], x)
        UD_x[1] = max(UD_x[1], x)
        U_y[0] = min(U_y[0], y)
        U_y[1] = max(U_y[1], y)
    elif(d == 'D'):
        UD_x[0] = min(UD_x[0], x)
        UD_x[1] = max(UD_x[1], x)
        D_y[0] = min(D_y[0], y)
        D_y[1] = max(D_y[1], y)
    elif(d == 'R'):
        LR_y[0] = min(LR_y[0], y)
        LR_y[1] = max(LR_y[1], y)
        R_x[0] = min(R_x[0], x)
        R_x[1] = max(R_x[1], x)
    elif(d == 'L'):
        LR_y[0] = min(LR_y[0], y)
        LR_y[1] = max(LR_y[1], y)
        L_x[0] = min(L_x[0], x)
        L_x[1] = max(L_x[1], x)

x_dif = max(UD_x[1], R_x[1], L_x[1]) - min(UD_x[0], R_x[0], L_x[0])
y_dif = max(LR_y[1], U_y[1], D_y[1]) - min(LR_y[0], U_y[0], D_y[0])
ans = x_dif * y_dif

check = []
if(D_y != [inf, -1*inf]):
    # D_y[0]
    for meet, speed in zip([LR_y[0], U_y[0]], [1,2] ):
        tmp = (D_y[0] - meet)/speed
        if(tmp > 0):
            check.append(tmp)
    # D_y[1]
    for meet, speed in zip([LR_y[1], U_y[1]], [1,2] ):
        tmp = (D_y[1] - meet)/speed
        if(tmp > 0):
            check.append(tmp)

if(D_y != [inf, -1*inf]):
    # D_y[0]
    for meet, speed in zip([LR_y[0], U_y[0]], [1,2] ):
        tmp = (D_y[0] - meet)/speed
        if(tmp > 0):
            check.append(tmp)
    # D_y[1]
    for meet, speed in zip([LR_y[1], U_y[1]], [1,2] ):
        tmp = (D_y[1] - meet)/speed
        if(tmp > 0):
            check.append(tmp)

if(U_y != [inf, -1*inf]):
    # U_y[0]
    for meet, speed in zip([LR_y[0], D_y[0]], [1,2] ):
        tmp = (meet - U_y[0])/speed
        if(tmp > 0):
            check.append(tmp)
    # U_y[1]
    for meet, speed in zip([LR_y[1], D_y[1]], [1,2] ):
        tmp = (meet - U_y[1])/speed
        if(tmp > 0):
            check.append(tmp)

if(L_x != [inf, -1*inf]):
    # L_x[0]
    for meet, speed in zip([UD_x[0], R_x[0]], [1,2] ):
        tmp = (L_x[0] - meet)/speed
        if(tmp > 0):
            check.append(tmp)
    # L_x[1]
    for meet, speed in zip([UD_x[1], R_x[1]], [1,2] ):
        tmp = (L_x[1] - meet)/speed
        if(tmp > 0):
            check.append(tmp)

if(R_x != [inf, -1*inf]):
    # R_x[0]
    for meet, speed in zip([UD_x[0], L_x[0]], [1,2] ):
        tmp = (meet - R_x[0])/speed
        if(tmp > 0):
            check.append(tmp)
    # R_x[1]
    for meet, speed in zip([UD_x[1], L_x[1]], [1,2] ):
        tmp = (meet - R_x[1])/speed
        if(tmp > 0):
            check.append(tmp)

for sec in check:
    x_dif = (max(UD_x[1], R_x[1]+sec, L_x[1]-sec)
            - min(UD_x[0], R_x[0]+sec, L_x[0]-sec))
    y_dif = (max(LR_y[1], U_y[1]+sec, D_y[1]-sec)
            - min(LR_y[0], U_y[0]+sec, D_y[0]-sec))
    ans = min(ans,x_dif * y_dif)

print(ans)