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 JAVA):

Solution:
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		long[] U = new long[n];
		long[] V = new long[n];
		for(int i=0;i<n;i++) {
			long x = in.nextLong();
			long y = in.nextLong();
			U[i] = x + y + (1L<<31);
			V[i] = x - y + (1L<<31);
		}
		in.close();
		long mod2 = U[0] % 2;
		boolean sameMod = true;
		for(int i=1;i<n;i++) {
			if(U[i]%2!=mod2) {
				sameMod = false;
				break;
			}
		}
		if(sameMod) {
			if(mod2==1) {
				long[] d = new long[31];
				System.out.println(31);
				
				String arms = "";
				for(int i=0;i<31;i++) {
					d[i] = 1L<<i;
					arms += d[i];
					arms += " ";
				}
				System.out.println(arms);
				
				for(int i=0;i<n;i++) {
					U[i] = (U[i] - 1)/2;
					V[i] = (V[i] - 1)/2;
					
					String ans = "";
					for(int j=0;j<31;j++) {
						long u = (U[i]>>j)&1;
						long v = (V[i]>>j)&1;
						if(u==1 && v==1) ans += "R";
						else if(u==0 && v==1) ans += "D";
						else if(u==1 && v==0) ans += "U";
						else if(u==0 && v==0) ans += "L";
					}
					System.out.println(ans);
				}
			}else {
				long[] d = new long[31];
				System.out.println(32);
				
				String arms = "";
				for(int i=0;i<31;i++) {
					d[i] = 1L<<i;
					arms += d[i];
					arms += " ";
				}
				arms += "1";
				System.out.println(arms);
				
				for(int i=0;i<n;i++) {
					U[i] = U[i]/2;
					V[i] = V[i]/2;
					
					String ans = "";
					for(int j=0;j<31;j++) {
						long u = (U[i]>>j)&1;
						long v = (V[i]>>j)&1;
						if(u==1 && v==1) ans += "R";
						else if(u==0 && v==1) ans += "D";
						else if(u==1 && v==0) ans += "U";
						else if(u==0 && v==0) ans += "L";
					}
					ans += "L";
					System.out.println(ans);
				}
			}
			
		}else {
			System.out.println(-1);
		}

	}

}