Robot

A robot is placed on a field modeled as an $n \times m$ grid. Some of the grid cells are walls.

The robot accepts four types of instructions: up, down, left, right.

Suppose the robot is currently at the coordinate $(x, y)$. Then the effect of executing each instruction is as follows.

• up: If $x = 0$ or $(x - 1, y)$ is a wall, the robot does not move. Otherwise, the robot moves to $(x - 1, y)$.
• down: If $x = n - 1$ or $(x + 1, y)$ is a wall, the robot does not move. Otherwise, the robot moves to $(x + 1, y)$.
• left: If $y = 0$ or $(x, y - 1)$ is a wall, the robot does not move. Otherwise, the robot moves to $(x, y - 1)$.
• right: If $y = m - 1$ or $(x, y + 1)$ is a wall, the robot does not move. Otherwise, the robot moves to $(x, y + 1)$.

You know that the starting position of the robot is either $(a, b)$ or $(c, d)$. Find a sequence of at most $q$ instructions such that the robot always ends up at $(0, 0)$ whether it starts from $(a, b)$ or from $(c, d)$. It can be proven that a solution exists for every input satisfying the problem constraints.

• $1 \le n \le 10$
• $1 \le m \le 10$
• $0 \le a \le n - 1$
• $0 \le b \le m - 1$
• $0 \le c \le n - 1$
• $0 \le d \le m - 1$
• $g[0][0] = g[a][b] = g[c][d] = 0$
• There exists a finite sequence of instructions to move the robot from $(a, b)$ to $(0, 0)$
• There exists a finite sequence of instructions to move the robot from $(c, d)$ to $(0, 0)$
• $q = 700$