You are given an $n \times n$ integer matrix board representing a Snakes and Ladders game. The cells correspond to squares labeled from $1$ to $n^2$ in a boustrophedon order: labeling starts at the bottom left cell, proceeds left to right across the bottom row, then continues on the next row up right to left, alternating direction each row until reaching the top row.

The game is played as follows:

• You start on square $1$.

• In one move, you roll a die and choose a destination square with a label in the range from your current label + $1$ to your current label + $6$, without exceeding $n^2$.

• After moving to that square, if the corresponding cell in board contains a value other than $-1$, you must immediately move to the square with that label. Otherwise, you remain on the square you moved to.

Return the minimum number of moves required to reach square $n^2$. If it is not possible to reach square $n^2$, return $-1$.

Note: If the destination of a snake or ladder is the start of another snake or ladder, only the first jump is applied. For example, if 2 → 5 and 5 → 8, landing on 2 moves you to 5, not 8.

Constraints:

• n == board.length == board[i].length

• $2 \leq$ n $\leq 20$

• board[i][j] is either $-1$ or in the range $\left[1, n^2\right]$

• The squares labeled $1$ and $n^2$ are not the starting points of any snake or ladder.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.