Problem: Snuke is introducing a robot arm with the following properties to his factory:

* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).



Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).

Constraints

* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N
X_1 Y_1
X_2 Y_2
:
X_N Y_N


Output

If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.


m
d_1 d_2 ... d_m
w_1
w_2
:
w_N


m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.

w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.

Examples

Input

3
-1 0
0 3
2 -1


Output

2
1 2
RL
UU
DR


Input

5
0 0
1 0
2 0
3 0
4 0


Output

-1


Input

2
1 1
1 1


Output

2
1 1
RU
UR


Input

3
-7 -3
7 3
-3 -7


Output

5
3 1 4 1 5
LRDUL
RDULR
DULRD

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define per(i,a,b) for(int i=(a);i>=(b);--i)
#define int long long 
using namespace std;
const int N=1e3+7,M=31;
int n,x[N],y[N],f[N],tot;
string s;
void work(int dx,int dy){
	int nx=0,ny=0;
	per(i,tot,1){
		int tx=dx-nx,ty=dy-ny;
		if(abs(tx)>abs(ty)){
			if(tx>0)s="R"+s,nx+=f[i];
			else s="L"+s,nx-=f[i];
		}
		else {
			if(ty>0)s="U"+s,ny+=f[i];
			else s="D"+s,ny-=f[i];
		}
	}
}
signed main(){
	cin>>n;
	rep(i,1,n)cin>>x[i]>>y[i];
	
	rep(i,2,n)if(abs(x[1]+y[1]-x[i]-y[i])&1){cout<<-1;return 0;}
	if((x[1]+y[1])&1){f[1]=1;rep(i,2,31)f[i]=f[i-1]<<1;tot=31;}
	else {f[1]=f[2]=1;rep(i,3,32)f[i]=f[i-1]<<1;tot=32;}
	
	cout<<tot<<endl;
	rep(i,1,tot)cout<<f[i]<<" ";
	cout<<endl;
	
	rep(i,1,n){
		s="";
		work(x[i],y[i]);
		cout<<s<<endl;
	}
	return 0;
}