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
int MAX=1000000007;



signed main() {
int n;
cin>>n;
long double x,y;
char d;
long double maxx=-1*MAX,minx=MAX,maxy=-1*MAX,miny=MAX,lmaxx=-1*MAX,lminx=MAX,rmaxx=-1*MAX,rminx=MAX,umaxy=-1*MAX,uminy=MAX,dmaxy=-1*MAX,dminy=MAX;
for(int i=0;i<n;i++){
    cin>>x>>y>>d;
    if(d=='R'){
        maxy=max(maxy,y);
        miny=min(miny,y);
        rmaxx=max(rmaxx,x);
        rminx=min(rminx,x);
    }
    if(d=='L'){
        maxy=max(maxy,y);
        miny=min(miny,y);
        lmaxx=max(lmaxx,x);
        lminx=min(lminx,x);
    }
    if(d=='U'){
        umaxy=max(umaxy,y);
        uminy=min(uminy,y);
        maxx=max(maxx,x);
        minx=min(minx,x);
    }
    if(d=='D'){
        dmaxy=max(dmaxy,y);
        dminy=min(dminy,y);
        maxx=max(maxx,x);
        minx=min(minx,x);
    }
}
long double ans=(max(maxx,max(rmaxx,lmaxx))-min(minx,min(lminx,rminx)))*(max(maxy,max(umaxy,dmaxy))-min(miny,min(uminy,dminy)));
long double a=max(maxx,max(rmaxx,lmaxx))-min(minx,min(lminx,rminx)),b=max(maxy,max(umaxy,dmaxy))-min(miny,min(uminy,dminy));
rmaxx+=0.5;lmaxx-=0.5;rminx+=0.5;lminx-=0.5;umaxy+=0.5;uminy+=0.5;dmaxy-=0.5;dminy-=0.5;
while(a>max(maxx,max(rmaxx,lmaxx))-min(minx,min(lminx,rminx))||b>max(maxy,max(umaxy,dmaxy))-min(miny,min(uminy,dminy))){
    ans=min(ans,(max(maxx,max(rmaxx,lmaxx))-min(minx,min(lminx,rminx)))*(max(maxy,max(umaxy,dmaxy))-min(miny,min(uminy,dminy))));
  a=max(maxx,max(rmaxx,lmaxx))-min(minx,min(lminx,rminx));b=max(maxy,max(umaxy,dmaxy))-min(miny,min(uminy,dminy));
rmaxx+=0.5;lmaxx-=0.5;rminx+=0.5;lminx-=0.5;umaxy+=0.5;uminy+=0.5;dmaxy-=0.5;dminy-=0.5;
}
cout<<setprecision(12)<<ans;

 
   

      return 0;

}