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 scanner = new Scanner(System.in);

    int N = scanner.nextInt();
    int[] u = new int[N];
    int[] v = new int[N];
    for (int i = 0; i < N; i++) {
      int x = scanner.nextInt();
      int y = scanner.nextInt();
      u[i] = x + y;
      v[i] = x - y;
    }

    int r = Math.abs(u[0] % 2);
    for (int i = 1; i < N; i++) {
      if (Math.abs(u[i] % 2) != r) {
        System.out.println("-1");
        return;
      }
    }
    r = 1 - r;

    int m = 31;
    System.out.println(m + r);
    StringBuilder sb = new StringBuilder();
    if (r > 0) System.out.print("1 ");
    for (int i = 0; i < m; i++) {
      int d = 1 << i;
      sb.append(d);
      if (i < m - 1) sb.append(' ');
    }
    System.out.println(sb.toString());

    long base = (1L << m) - 1 - r;
    char[] d = new char[]{'L', 'D', 'U', 'R'};
    for (int i = 0; i < N; i++) {
      sb.setLength(0);
      if (r > 0) sb.append('R');
      long uu = (u[i] + base) / 2;
      long vv = (v[i] + base) / 2;
      for (int j = 0; j < m; j++) {
        int u1 = (int) Math.abs(uu % 2);
        int v1 = (int) Math.abs(vv % 2);
        sb.append(d[u1 * 2 + v1]);
        uu /= 2;
        vv /= 2;
      }
      if (uu != 0 || vv != 0) throw new IllegalStateException();
      System.out.println(sb.toString());
    }
  }
}