Bobo has been playing a puzzle called Rolling Stones, which takes place on an equilateral triangular board consisting of $$$n$$$ $$$(n\geq 2)$$$ rows and $$$n^2$$$ cells. Each cell on the board is labeled with a number from $$$1$$$ to $$$4$$$. Bobo also has a tetrahedral stone, with each face numbered from $$$1$$$ to $$$4$$$ (a tetrahedral dice), initially placed at the first cell in the first row of the board. The position of the stone is as follows: the face with the number $$$1$$$ is towards the left, the face with the number $$$2$$$ is towards the next row, the face with the number $$$3$$$ is towards the right, and the face with the number $$$4$$$ is on the bottom side.
The goal of the puzzle is to roll the stone to a target cell under the following rules:
- Matching Numbers: When the stone rests on a cell, the number on the cell must match the number on the stone's bottom face.
- Single Visit: Each cell can only be visited once throughout the journey, including the starting and target cells.
The illustration for a solution of the first sample test is given as follows.
Illustration The first line contains an integer $$$n$$$ $$$(2\leq n\leq 100)$$$, denoting the size of the board.
Then $$$n$$$ lines follows, with the $$$i$$$-th $$$(1\leq i\leq n)$$$ line containing $$$2i-1$$$ numbers $$$a_{i,1},a_{i,2},\dots,a_{i,2i-1}$$$, where each $$$1\leq a_{i,j}\leq 4$$$ indicates the number on the $$$j$$$-th cell from left to right in the $$$i$$$-th row. It is guaranteed that $$$a_{1,1}=4$$$.
Then another line follows, containing two integers $$$x,y$$$ $$$(2\leq x\leq n,1\leq y\leq 2x-1)$$$. Here, $$$(x,y)$$$ represents the target cell, located at the $$$y$$$-th cell from left to right in the $$$x$$$-th row.
If there is no way to roll the stone to the target cell, output $$$-1$$$ in a line. Otherwise, output the minimum number of rolls to roll the stone to the target cell in a line.
343 2 34 3 2 1 33 1
6
343 3 34 3 2 1 33 1
-1
