{"raw_statement":[{"iden":"problem statement","content":"Snuke is introducing a **robot arm** with the following properties to his factory:\n\n*   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 $d_i$.\n*   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 $(x_i, y_i)$):\n    *   $(x_0, y_0) = (0, 0)$.\n    *   If the mode of Section $i$ is `L`, $(x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1})$.\n    *   If the mode of Section $i$ is `R`, $(x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1})$.\n    *   If the mode of Section $i$ is `D`, $(x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i})$.\n    *   If the mode of Section $i$ is `U`, $(x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i})$.\n\nSnuke 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 $(X_j, Y_j)$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 1000$\n*   $-10^9 \\leq X_i \\leq 10^9$\n*   $-10^9 \\leq Y_i \\leq 10^9$"},{"iden":"partial score","content":"*   In the test cases worth $300$ points, $-10 \\leq X_i \\leq 10$ and $-10 \\leq Y_i \\leq 10$ hold."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$X_1$ $Y_1$\n$X_2$ $Y_2$\n$:$\n$X_N$ $Y_N$"},{"iden":"sample input 1","content":"3\n-1 0\n0 3\n2 -1"},{"iden":"sample output 1","content":"2\n1 2\nRL\nUU\nDR\n\nIn the given way to bring Joint $m$ of the robot arm to each $(X_j, Y_j)$, the positions 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 $(X_3, Y_3) = (2, -1)$: $(x_0, y_0) = (0, 0), (x_1, y_1) = (0, -1), (x_2, y_2) = (2, -1)$."},{"iden":"sample input 2","content":"5\n0 0\n1 0\n2 0\n3 0\n4 0"},{"iden":"sample output 2","content":"\\-1"},{"iden":"sample input 3","content":"2\n1 1\n1 1"},{"iden":"sample output 3","content":"2\n1 1\nRU\nUR\n\nThere may be duplicated points among $(X_j, Y_j)$."},{"iden":"sample input 4","content":"3\n-7 -3\n7 3\n-3 -7"},{"iden":"sample output 4","content":"5\n3 1 4 1 5\nLRDUL\nRDULR\nDULRD"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}