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>
const int INF=1e9;
const int MOD=1e9+7;
//const int MOD=998244353;
const long long LINF=1e18;
using namespace std;
#define int long double
//template

//main
signed main(){
  int N;cin>>N;
  std::vector<int> x(N),y(N);
  std::vector<char> q(N);
  for(int i=0;i<N;i++)cin>>x[i]>>y[i]>>q[i];
  char u,d,l,r;u='U';d='D';l='L';r='R';
  int uyM,uym,dyM,dym,lyM,lym;
  int lxM,lxm,rxM,rxm,uxM,uxm;
  uyM=dyM=lyM=lxM=rxM=uxM=-LINF;
  uym=dym=lym=lxm=rxm=uxm=LINF;
  for(int i=0;i<N;i++){
    if(q[i]==u){
      uyM=max(uyM,y[i]);
      uym=min(uym,y[i]);
      uxM=max(uxM,x[i]);
      uxm=min(uxm,x[i]);
    }
    if(q[i]==l){
      lyM=max(lyM,y[i]);
      lym=min(lym,y[i]);
      lxM=max(lxM,x[i]);
      lxm=min(lxm,x[i]);
    }
    if(q[i]==d){
      dyM=max(dyM,y[i]);
      dym=min(dym,y[i]);
      uxM=max(uxM,x[i]);
      uxm=min(uxm,x[i]);
    }
    if(q[i]==r){
      lyM=max(lyM,y[i]);
      lym=min(lym,y[i]);
      rxM=max(rxM,x[i]);
      rxm=min(rxm,x[i]);
    }
  }
  int yMult,yMudt,yMdlt;
  int ymult,ymudt,ymdlt;
  int xMrut,xMlut,xMrlt;
  int xmrut,xmlut,xmrlt;

  std::vector<int> t(2e7+15,0);
  t[0]=lym-uym;
  t[1]=(dym-uym)/2;
  t[2]=dyM-lyM;
  t[3]=(dyM-uyM)/2;
  t[4]=lxM-uxM;
  t[5]=(lxM-rxM)/2;
  t[6]=uxm-rxm;
  t[7]=(lxm-rxm)/2;
  t[8]=lyM-uyM;
  t[10]=dym-lym;
  t[12]=lxm-uxm;
  t[14]=uxM-rxM;
  for(int i=15;i<2e7+15;i++)t[i]=i*5;
  int ans=LINF;
  for(int i=0;i<2e7+15;i++){
    if(t[i]<0)continue;
    int xM=max({uxM,lxM-t[i],rxM+t[i]});
    int xm=min({uxm,lxm-t[i],rxm+t[i]});
    int yM=max({uyM+t[i],lyM,dyM-t[i]});
    int ym=min({uym+t[i],lym,dym-t[i]});
    ans=min(ans,(xM-xm)*(yM-ym));
  }
  cout<<fixed<<setprecision(12)<<ans<<endl;
}