<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>

class Solution:
    def minimumMoves(self, grid: List[List[int]]) -> int:
        grid = [[1] * (len(grid[0])+2)] + \
               [[1] + grid[i] + [1] for i in range(len(grid))] + \
               [[1]*(len(grid[0])+2)]
        R, C = len(grid), len(grid[0])
        def canrotate(r, c):
            if grid[r][c] == grid[r][c+1] == grid[r+1][c] == grid[r+1][c+1] == 0:
                return True
        #state 1: horizontal    state 2: vertical
        def dfs(r, c, state):
            if state&1 and r==R-2 and c==C-3: return 0
            if (r, c, state) in memo: return memo[(r, c, state)]
            memo[(r, c, state)] = res = 10**8
            if state&1:
                if grid[r][c+2] == 0: res = min(res, dfs(r, c+1, 1)+1)
                if grid[r+1][c] == 0 and grid[r+1][c+1] == 0: res = min(res, dfs(r+1, c, 1)+1)
            if state&2:
                if grid[r][c+1] == 0 and grid[r+1][c+1] == 0: res = min(res, dfs(r, c+1, 2)+1) 
                if grid[r+2][c] == 0: res = min(res, dfs(r+1, c, 2)+1)
            if grid[r][c] == grid[r][c+1] == grid[r+1][c] == grid[r+1][c+1] == 0:
                res = min(res, dfs(r, c, 3-state)+1)
            memo[(r, c, state)] = res
            return res
        memo = {}
        return dfs(1, 1, 1) if dfs(1, 1, 1) != 10**8 else -1
23500