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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[][] x = new int[n][2];
        int mod = 0;
        for(int i=0; i<n; i++){
            x[i][0] = sc.nextInt();
            x[i][1] = sc.nextInt();
            if(i == 0){
                mod = Math.abs(x[i][0] + x[i][1]) % 2;
            }else{
                if(Math.abs(x[i][0] + x[i][1]) % 2 != mod){
                    System.out.println(-1);
                    return;
                }
            }
        }
        sc.close();

        long[] pow3 = new long[25];
        pow3[0] = 1;
        for(int i=1; i<25; i++){
            pow3[i] = pow3[i-1] * 3;
        }

        int m;
        long[] arm;
        if(mod == 1){
            m = 40;
            arm = new long[m];
            for(int i=0; i<19; i++){
                arm[i*2] = pow3[19 - i];
                arm[i*2+1] = pow3[18-i]*2;
            }
            arm[38] = 1;
            arm[39] = 1;
        }else{
            m = 39;
            arm = new long[m];
            for(int i=0; i<19; i++){
                arm[i*2] = pow3[19-i];
                arm[i*2+1] = pow3[18-i]*2;
            }
            arm[38] = 1;
        }

        // Arrays.fill(arm, 1);

        System.out.println(m);
        for(int i=0; i<m-1; i++){
            System.out.print(arm[i] + " ");
        }
        System.out.println(arm[m-1]);
        
        for(int i=0; i<n; i++){
            long cx = 0, cy = 0;
            long tx = x[i][0], ty = x[i][1];
            String ans = "";
            for(int j=0; j<m; j++){
                if(Math.abs(tx-cx) > Math.abs(ty-cy)){
                    if(tx > cx){
                        ans += "R";
                        cx += arm[j];       
                    }else{
                        ans += "L";
                        cx -= arm[j];
                    }
                }else{
                    if(ty > cy){
                        ans += "U";
                        cy += arm[j];
                    }else{
                        ans += "D";
                        cy -= arm[j];
                    }
                }
            }
            System.out.println(ans);
            // System.out.println(ans + " " + cx + " " + cy);
        }
    }
}