Hamiltonian Tour on Grid

Given an $n\times n$ grid and a starting cell $(r, c)$ (1-indexed), determine whether it is possible to perform a Hamiltonian tour — a path that visits every cell exactly once and returns to the starting cell. A valid tour must be represented as a sequence of moves: U (up), D (down), L (left), and R (right).

For this problem, a valid tour exists only for a $1\times 1$ grid where no moves are needed. For any grid with $n > 1$, output impossible.

inputFormat

Input is read from stdin as three space-separated integers: $r$, $c$, and $n$. Here, $r$ and $c$ represent the starting row and column (with 1-indexing), and $n$ specifies the size of the grid (i.e. the grid is $n\times n$).

outputFormat

Output a single string to stdout representing the move sequence if a Hamiltonian tour exists; otherwise, output impossible. For a $1\times 1$ grid, output an empty string.## sample

1 1 1