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:
n = int(input())
R = []
L = []
U = []
D = []
lm = [float("INF")]*3
rm = [-float("INF")]*3
dm = [float("INF")]*3
um = [-float("INF")]*3
for i in range(n):
    x,y,d = input().split()
    x = int(x)
    y = int(y)
    if d == "U":
        rm[1] = max(rm[1],x)
        lm[1] = min(lm[1],x)
        dm[0] = min(dm[0],y)
        um[2] = max(um[2],y)
        U.append((x,y,d))
    elif d == "D":
        rm[1] = max(rm[1],x)
        lm[1] = min(lm[1],x)
        um[0] = max(um[0],y)
        dm[2] = min(dm[2],y)
        D.append((x,y,d))
    elif d == "L":
        um[1] = max(um[1],y)
        dm[1] = min(dm[1],y)
        rm[0] = max(rm[0],x)
        lm[2] = min(lm[2],x)
        L.append((x,y,d))
    else:
        um[1] = max(um[1],y)
        dm[1] = min(dm[1],y)
        lm[0] = min(lm[0],x)
        rm[2] = max(rm[2],x)
        R.append((x,y,d))
time = set()
def rc(t):
    if rm[2] == max(rm):
        return rm[2]+t
    if rm[1] == max(rm):
        if rm[2] == -float("INF"):
            return rm[1]
        else:
            time.add(rm[1]-rm[2])
            return max(rm[1],rm[2]+t)
    if rm[2] == -float("INF") and rm[1] == -float("INF"):
        return rm[0]-t
    if rm[2] == -float("INF"):
        time.add(rm[0]-rm[1])
        return max(rm[1],rm[0]-t)
    if rm[1] == -float("INF"):
        time.add((rm[0]-rm[2])/2)
        return max(rm[0]-t,rm[2]+t)
    if (rm[0]-rm[2])/2+rm[2] >= rm[1]:
        time.add((rm[0]-rm[2])/2)
        return max(rm[0]-t,rm[2]+t)
    time.add(rm[0]-rm[1])
    time.add(rm[1]-rm[2])
    return max(rm[0]-t,rm[2]+t,rm[1])
def lc(t):
    if lm[2] == min(lm):
        return lm[2]-t
    if lm[1] == min(lm):
        if lm[2] == float("INF"):
            return lm[1]
        else:
            time.add(-lm[1]+lm[2])
            return min(lm[1],lm[2]-t)
    if lm[2] == float("INF") and lm[1] == float("INF"):
        return lm[0]+t
    if lm[2] == float("INF"):
        time.add(-lm[0]+lm[1])
        return min(lm[1],lm[0]+t)
    if lm[1] == float("INF"):
        time.add((-lm[0]+lm[2])/2)
        return min(lm[0]+t,lm[2]-t)
    if lm[2]-(-lm[0]+lm[2])/2 <= lm[1]:
        time.add((-lm[0]+lm[2])/2)
        return min(lm[0]+t,lm[2]-t)
    time.add(-lm[0]+lm[1])
    time.add(-lm[1]+lm[2])
    return min(lm[0]+t,lm[2]-t,lm[1])
def uc(t):
    if um[2] == max(um):
        return um[2]+t
    if um[1] == max(um):
        if um[2] == -float("INF"):
            return um[1]
        else:
            time.add(um[1]-um[2])
            return max(um[1],um[2]+t)
    if um[2] == -float("INF") and um[1] == -float("INF"):
        return um[0]-t
    if um[2] == -float("INF"):
        time.add(um[0]-um[1])
        return max(um[1],um[0]-t)
    if um[1] == -float("INF"):
        time.add((um[0]-um[2])/2)
        return max(um[0]-t,um[2]+t)
    if (um[0]-um[2])/2+um[2] >= um[1]:
        time.add((um[0]-um[2])/2)
        return max(um[0]-t,um[2]+t)
    time.add(um[0]-um[1])
    time.add(um[1]-um[2])
    return max(um[0]-t,um[2]+t,um[1])
def dc(t):
    if dm[2] == min(dm):
        return dm[2]-t
    if dm[1] == min(dm):
        if dm[2] == float("INF"):
            return dm[1]
        else:
            time.add(-dm[1]+dm[2])
            return min(dm[1],dm[2]-t)
    if dm[2] == float("INF") and dm[1] == float("INF"):
        return dm[0]+t
    if dm[2] == float("INF"):
        time.add(-dm[0]+dm[1])
        return min(dm[1],dm[0]+t)
    if dm[1] == float("INF"):
        time.add((-dm[0]+dm[2])/2)
        return min(dm[0]+t,dm[2]-t)
    if dm[2]-(-dm[0]+dm[2])/2 <= dm[1]:
        time.add((-dm[0]+dm[2])/2)
        return min(dm[0]+t,dm[2]-t)
    time.add(-dm[0]+dm[1])
    time.add(-dm[1]+dm[2])
    return min(dm[0]+t,dm[2]-t,dm[1])
ans = (rc(0)-lc(0))*(uc(0)-dc(0))
for t in time:
    count = (rc(t)-lc(t))*(uc(t)-dc(t))
    ans = min(ans,count)
print(ans)