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 CPP):

Solution:
#include"bits/stdc++.h"
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
const long long MOD = 1000000007;
const long long inf = 1ll<<61;
const double eps = 0.000000000001;
typedef pair<int, int> P;
typedef pair<int ,P> PP;
struct edge { int to; int to2; int cost; };
double x[114514], y[114514];
char d[114514];
string SS = "LRUD";
int n; 
double tans(double t) {
	double mx = inf, MX = -inf, my = inf, MY = -inf;
	rep(i, n) {
		double nx, ny;
		if (d[i] == 'R') {
			nx = x[i] + t;
			ny = y[i];
		}
		if (d[i] == 'L') {
			nx = x[i] - t;
			ny = y[i];
		}
		if (d[i] == 'U') {
			nx = x[i];
			ny = y[i] + t;
		}
		if (d[i] == 'D') {
			nx = x[i];
			ny = y[i] - t;
		}
		mx = min(mx, nx);
		MX = max(MX, nx);
		my = min(my, ny);
		MY = max(MY, ny);
	}
	return (MX - mx)*(MY - my);
}

signed main() {
	cin >> n;
	rep(i, n)cin >> x[i] >> y[i] >> d[i];
	
/*	random_device rnd;
	mt19937 mt(rnd());
	rep(i, n) {
		x[i] = mt() % 200000000;
		x[i] -= 100000000;
		y[i] = mt() % 200000000;
		y[i] -= 100000000;
		d[i] = SS[mt() % 4];
	}*/


	double lb = 0, ub = 1e10;
	rep(i, 240) {
		double t1 = (2 * lb + ub) / 3;
		double t2 = (lb + 2 * ub) / 3;
		if (tans(t1)+eps < tans(t2))ub = t2;
		else lb = t1;
	}
//	printf("%.11lf\n", lb);
	printf("%.11lf\n", tans(lb));
}