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<iostream>
#include<cstdio>
#include<cstring>
#include<ctime>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<string>
#include<queue>
#include<vector>
#include<map>
#include<set>
#include<utility>
#include<iomanip>
using namespace std;
int read(){
    int xx=0,ff=1;char ch=getchar();
    while(ch>'9'||ch<'0'){if(ch=='-')ff=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){xx=xx*10+ch-'0';ch=getchar();}
    return xx*ff;
}
long long READ(){
    long long xx=0,ff=1;char ch=getchar();
    while(ch>'9'||ch<'0'){if(ch=='-')ff=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){xx=xx*10+ch-'0';ch=getchar();}
    return xx*ff;
}
char one(){
	char ch=getchar();
	while(ch==' '||ch=='\n')
		ch=getchar();
	return ch;
}
const int maxn=100010;
const int ws_[4]={1,-1,0,0},ad_[4]={0,0,1,-1};
int N;
struct point{
	double x,y;
	int dir;
	point(double xx=0,double yy=0,int dd=0){
		x=xx,y=yy,dir=dd;
	}
	point move(double t){
		return point(x+ws_[dir]*t,y+ad_[dir]*t,dir);
	}
}p[maxn];
double calc(double x){
	double mxx=-1e10,mxy=-1e10,mnx=1e10,mny=1e10;
	for(int i=1;i<=N;i++){
		point tmp=p[i].move(x);
		mxx=max(mxx,tmp.x);
		mxy=max(mxy,tmp.y);
		mnx=min(mnx,tmp.x);
		mny=min(mny,tmp.y);
	}
	return (mxx-mnx)*(mxy-mny);
}
int main(){
	//freopen("in","r",stdin);
	N=read();
	for(int i=1;i<=N;i++){
		p[i].x=read(),p[i].y=read();
		char ch=one();
		if(ch=='R')p[i].dir=0;
		else if(ch=='L')p[i].dir=1;
		else if(ch=='U')p[i].dir=2;
		else p[i].dir=3;
	}
	double L=0,R=1e12,mid1,mid2,val1,val2,ans=1e18;
	for(int i=1;i<=500;i++){
		mid1=L+(R-L)/3;
		mid2=R-(R-L)/3;
		val1=calc(mid1);
		val2=calc(mid2);
		if(val1>val2)
			L=mid1;
		else
			R=mid2;
		ans=min(ans,val1);
		ans=min(ans,val2);
	}
	printf("%.10lf\n",ans);
	return 0;
}