Hot Spot

Hot Spot is a single-player game played on a 4 by 4 board. The goal is to move a red robot from its current square to the top-left corner. The board may also contain green and blue robots. At any time, each square holds at most one robot.

A robot may move in one of two ways:

1. If two robots are adjacent horizontally or vertically (never diagonally), one may jump over the other into the square immediately beyond, provided that square is empty. For example, if robot $a$ is immediately to the left of robot $b$, then $a$ may jump to the square immediately to the right of $b$.
2. If three robots are in a row horizontally or vertically (again never diagonally), one of them may jump over the other two into the square immediately beyond, provided that square is empty. For example, if $b$ is immediately to the right of $a$ and $c$ is immediately to the right of $b$, then $a$ may jump to the square immediately to the right of $c$.

Every jump only changes the position of the jumping robot; robots are never removed from or added to the board.

A blue robot may never be adjacent, horizontally or vertically, to another blue robot or to the red robot; no move may create such an adjacency.

Given the initial board, determine the minimum number of jumps needed to bring the red robot to the top-left corner.

The input describes the initial board as four lines, each containing four characters. Each character is one of: R for the red robot, B for a blue robot, G for a green robot, or . (a period) for an empty square.

Output a single line with one integer: the minimum number of jumps needed for the red robot to reach the top-left square of the board.