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 ll long long
struct Point
{
    double x,y;
    int dx,dy;
};
double simulate(vector<Point> points,double t)
{
    double maxX=-1e18,maxY=-1e18,minX=1e18,minY=1e18;
    for(int i=0;i<points.size();++i)
    {
        points[i].x += points[i].dx * t;
        points[i].y += points[i].dy * t;
        maxX = max(maxX,points[i].x);
        maxY = max(maxY,points[i].y);
        minX = min(minX,points[i].x);
        minY = min(minY,points[i].y);
    }
    return (maxY-minY)*(maxX-minX);
}
int main()
{
    int n;
    cin>>n;
    vector<Point> points(n);
    for(int i=0;i<n;++i)
    {
        cin>>points[i].x>>points[i].y;
        char ch;
        cin>>ch;
        if(ch == 'U')
        {
            points[i].dx = 0, points[i].dy = 1;
        }else if(ch == 'D')
        {
            points[i].dx = 0, points[i].dy = -1;
        }else if(ch == 'L')
        {
            points[i].dx = -1, points[i].dy = 0;
        }
        else if(ch == 'R')
        {
            points[i].dx = 1, points[i].dy = 0;
        }
    }
    double l = 0, r = 1e8;
    while(l+1e-8<r){
        double m1=l+(r-l)/3;
        double m2=r-(r-l)/3;
        if(-simulate(points, m1)>-simulate(points, m2))
            r=m2;
        else
            l=m1;
    }
    printf("%.9f\n",simulate(points,l));
}