<p>In an&nbsp;<code>n*n</code>&nbsp;grid, there is a snake that spans 2 cells and starts moving from the top left corner at <code>(0, 0)</code> and <code>(0, 1)</code>. The grid has empty cells represented by zeros and blocked cells represented by ones. The snake wants to reach the lower right corner at&nbsp;<code>(n-1, n-2)</code>&nbsp;and&nbsp;<code>(n-1, n-1)</code>.</p>

<p>In one move the snake can:</p>

<ul>
	<li>Move one cell to the right&nbsp;if there are no blocked cells there. This move keeps the horizontal/vertical position of the snake as it is.</li>
	<li>Move down one cell&nbsp;if there are no blocked cells there. This move keeps the horizontal/vertical position of the snake as it is.</li>
	<li>Rotate clockwise if it&#39;s in a horizontal position and the two cells under it are both empty. In that case the snake moves from&nbsp;<code>(r, c)</code>&nbsp;and&nbsp;<code>(r, c+1)</code>&nbsp;to&nbsp;<code>(r, c)</code>&nbsp;and&nbsp;<code>(r+1, c)</code>.<br />
	<img alt="" src="https://assets.leetcode.com/uploads/2019/09/24/image-2.png" style="width: 300px; height: 134px;" /></li>
	<li>Rotate counterclockwise&nbsp;if it&#39;s in a vertical position and the two cells to its right are both empty. In that case the snake moves from&nbsp;<code>(r, c)</code>&nbsp;and&nbsp;<code>(r+1, c)</code>&nbsp;to&nbsp;<code>(r, c)</code>&nbsp;and&nbsp;<code>(r, c+1)</code>.<br />
	<img alt="" src="https://assets.leetcode.com/uploads/2019/09/24/image-1.png" style="width: 300px; height: 121px;" /></li>
</ul>

<p>Return the minimum number of moves to reach the target.</p>

<p>If there is no way to reach the target, return&nbsp;<code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/24/image.png" style="width: 400px; height: 439px;" /></strong></p>

<pre>
<strong>Input:</strong> grid = [[0,0,0,0,0,1],
               [1,1,0,0,1,0],
&nbsp;              [0,0,0,0,1,1],
&nbsp;              [0,0,1,0,1,0],
&nbsp;              [0,1,1,0,0,0],
&nbsp;              [0,1,1,0,0,0]]
<strong>Output:</strong> 11
<strong>Explanation:
</strong>One possible solution is [right, right, rotate clockwise, right, down, down, down, down, rotate counterclockwise, right, down].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[0,0,1,1,1,1],
&nbsp;              [0,0,0,0,1,1],
&nbsp;              [1,1,0,0,0,1],
&nbsp;              [1,1,1,0,0,1],
&nbsp;              [1,1,1,0,0,1],
&nbsp;              [1,1,1,0,0,0]]
<strong>Output:</strong> 9
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 100</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 1</code></li>
	<li>It is guaranteed that the snake starts at empty cells.</li>
</ul>

from collections import deque
from typing import List

class Solution:
    def minimumMoves(self, grid: List[List[int]]) -> int:
        n = len(grid)
        que = deque([((0, 0), (0, 1), 0)])  # (tail, head, moves)
        visited = set([((0, 0), (0, 1))])  # Track visited states of (tail, head)

        while que:
            (tail_y, tail_x), (head_y, head_x), moves = que.popleft()

            # Check if we have reached the final position
            if (head_y, head_x) == (n - 1, n - 1) and (tail_y, tail_x) == (n - 1, n - 2):
                return moves

            # Move right
            if head_x + 1 < n and grid[tail_y][tail_x + 1] == 0 and grid[head_y][head_x + 1] == 0:
                new_state = ((tail_y, tail_x + 1), (head_y, head_x + 1)) 
                if new_state not in visited:
                    visited.add(new_state)
                    que.append((new_state[0], new_state[1], moves + 1))
            
            # Move down
            if head_y + 1 < n and tail_y + 1 < n and grid[head_y + 1][head_x] == 0 and grid[tail_y + 1][tail_x] == 0:
                new_state = ((tail_y + 1, tail_x), (head_y + 1, head_x))
                if new_state not in visited:
                    visited.add(new_state)
                    que.append((new_state[0], new_state[1], moves + 1))
                
            # Rotate clockwise (horizontal to vertical)
            if tail_y == head_y and head_y + 1 < n and grid[head_y + 1][head_x] == 0 and grid[tail_y + 1][tail_x] == 0:
                new_state = ((tail_y, tail_x), (tail_y + 1, tail_x))
                if new_state not in visited:
                    visited.add(new_state)
                    que.append((new_state[0], new_state[1], moves + 1))

            # Rotate counterclockwise (vertical to horizontal)
            if tail_x == head_x and head_x + 1 < n and grid[head_y][head_x + 1] == 0 and grid[tail_y][tail_x + 1] == 0:
                new_state = ((tail_y, tail_x), (tail_y, tail_x + 1))
                if new_state not in visited:
                    visited.add(new_state)
                    que.append((new_state[0], new_state[1], moves + 1))

        return -1  # If no solution is found

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