output_description: 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.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      X_1 Y_1
      X_2 Y_2
      :
      X_N Y_N
attempt: print(-1)
  
problem_description: Statement
  
  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).
samples: [{"input": "3\n    -1 0\n    0 3\n    2 -1", "output": "2\n    1 2\n    RL\n    UU\n    DR\n    \n\nIn the given way to bring Joint m of the robot arm to each (X_j, Y_j), the\npositions of the joints will be as follows:\n\n  * To (X_1, Y_1) = (-1, 0): First, the position of Joint 0 is (x_0, y_0) = (0, 0). As the mode of Section 1 is `R`, the position of Joint 1 is (x_1, y_1) = (1, 0). Then, as the mode of Section 2 is `L`, the position of Joint 2 is (x_2, y_2) = (-1, 0).\n  * To (X_2, Y_2) = (0, 3): (x_0, y_0) = (0, 0), (x_1, y_1) = (0, 1), (x_2, y_2) = (0, 3).\n  * To (X_3, Y_3) = (2, -1): (x_0, y_0) = (0, 0), (x_1, y_1) = (0, -1), (x_2, y_2) = (2, -1).\n\n* * *"}, {"input": "5\n    0 0\n    1 0\n    2 0\n    3 0\n    4 0", "output": "-1\n    \n\n* * *"}, {"input": "2\n    1 1\n    1 1", "output": "2\n    1 1\n    RU\n    UR\n    \n\nThere may be duplicated points among (X_j, Y_j).\n\n* * *"}, {"input": "3\n    -7 -3\n    7 3\n    -3 -7", "output": "5\n    3 1 4 1 5\n    LRDUL\n    RDULR\n    DULRD"}]