The picture shows the chessboard. The move of the chess piece "Ma" is as follows: start from one square, jump 2 squares horizontally or vertically, jump 1 square in the other direction, and walk out of a "day" shape. For example, you can reach any position of B by taking one step from A in the picture ... So, what are the fastest ways for the chess piece "horse" to jump from the lower left corner to the upper right corner?

analyse

On the chess board, each box has a standard code name. For example, the black grid at the lower left represents the white grid at the lower right, and the black grid at the upper right is the code.

Mathematically speaking, for convenience, the grid in the lower left corner can be written, the grid in the upper right corner can be written, and the grid next to the diagonal in the upper right corner can be written.

The typical fastest way from to is as follows:

The characteristics of the above method are: each step is progressive horizontally and vertically, which meets the requirements of the "fastest method".

A typical walk from to is as follows:

The above method also meets the requirements of the fastest method, and its characteristic is that both vertical and horizontal directions are three, two and one.

For convenience, we introduce the following symbols:

The typical walk from to mentioned above can be simply expressed as:

This movement is variable, and its final effect is the same, that is, the horizontal forward grid and the vertical forward grid.

In order to reach the black square in the upper right corner, two more steps are needed: one step and one step, which can neither be the first step nor the last step.

Specific examples are:

Using interpolation model, we can get this kind of walking.