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 <stdio.h>
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf 10000000000000

int main(){
	
	int N;
	cin>>N;
	
	vector<long long> X(N),Y(N);
	
	rep(i,N){
		long long x,y;
		cin>>x>>y;
		X[i] = x+y;
		Y[i] = x-y;
	}
	
	rep(i,N){
		if(abs(X[i]%2)!=abs(X[0]%2)){
			cout<<-1<<endl;
			return 0;
		}
	}
	rep(j,N){
		for(long long i=0;i<35;i++){
			X[j] += (1LL<<i);
			Y[j] += (1LL<<i);
		}
	}
	
	int sz = 35;
	if(X[0]%2!=0)sz++;
	cout<<sz<<endl;
	vector<long long> t;
	if(X[0]%2!=0)t.push_back(1);
	for(long long i=0;i<35;i++)t.push_back((1LL)<<i);
	rep(i,t.size()){
		if(i!=0)cout<<' ';
		cout<<t[i];
	}
	cout<<endl;
	rep(i,N){
		string ans = "";
		if(X[i]%2!=0){
			ans += 'R';
			X[i] --;
			Y[i] --;
		}
		X[i]/=2;
		Y[i]/=2;
		
		for(long long j=0;j<35;j++){
			int a = (X[i]>>j)&1;
			int b = (Y[i]>>j)&1;
			if(a&&b)ans += 'R';
			if(!a&&!b)ans += 'L';
			if(a&&!b)ans += 'U';
			if(!a&&b)ans += 'D';
		}
		
		cout<<ans<<endl;
		
	}
	
	
    return 0;
}