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:
inf = float('inf')
N = int(input())
MRp = -inf
MR = -inf
MRm = -inf
mRp = inf
mR = inf
mRm = inf
MUp = -inf
MU = -inf
MUm = -inf
mUp = inf
mU = inf
mUm = inf

for i in range(N):
	x, y, d = input().split()
	x, y = int(x), int(y)
	if d == 'R':
		MRp = max(MRp, x)
		mRp = min(mRp, x)
		MU = max(MU, y)
		mU = min(mU, y)
	elif d == 'L':
		MRm = max(MRm, x)
		mRm = min(mRm, x)
		MU = max(MU, y)
		mU = min(mU, y)
	elif d == 'U':
		MUp = max(MUp, y)
		mUp = min(mUp, y)
		MR = max(MR, x)
		mR = min(mR, x)
	else:
		MUm = max(MUm, y)
		mUm = min(mUm, y)
		MR = max(MR, x)
		mR = min(mR, x)

t = [0]
if MR > max(MRp, MRm):
	t.append(MR - MRp)
elif MRm + MRp >= 2 * MR and MRm > MRp:
	t.append((MRm - MRp) / 2)
elif MRm > MRp:
	t.append(MRm - MR)
	t.append(MR - MRp)	
if mR < min(mRp, mRm):
	t.append(mRm - mR)
elif mRm + mRp <= 2 * mR and mRm > mRp:
	t.append((mRm - mRp) / 2)
elif mRm > mRp:
	t.append(mRm - mR)
	t.append(mR - mRp)
if MU > max(MUp, MUm):
	t.append(MU - MUp)
elif MUm + MUp >= 2 * MU and MUm > MUp:
	t.append((MUm - MUp) / 2)
elif MUm > MUp:
	t.append(MUm - MU)
	t.append(MU - MUp)
if mU < min(mUp, mUm):
	t.append(mUm - mU)
elif mUm + mUp <= 2 * mU and mUm > mUp:
	t.append((mUm - mUp) / 2)
elif mUm > mUp:
	t.append(mUm - mU)
	t.append(mU - mUp)

ans = inf
for i in t:
	dx = max(MRp + i, MR, MRm - i) - min(mRp + i, mR, mRm - i)
	dy = max(MUp + i, MU, MUm - i) - min(mUp + i, mU, mUm - i)
	ans = min(ans, dx * dy)
print(ans)