<p>You are given a <strong>0-indexed</strong> 2D integer matrix <code>grid</code> of size <code>3 * 3</code>, representing the number of stones in each cell. The grid contains exactly <code>9</code> stones, and there can be <strong>multiple</strong> stones in a single cell.</p>

<p>In one move, you can move a single stone from its current cell to any other cell if the two cells share a side.</p>

<p>Return <em>the <strong>minimum number of moves</strong> required to place one stone in each cell</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2023/08/23/example1-3.svg" style="width: 401px; height: 281px;" />
<pre>
<strong>Input:</strong> grid = [[1,1,0],[1,1,1],[1,2,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> One possible sequence of moves to place one stone in each cell is: 
1- Move one stone from cell (2,1) to cell (2,2).
2- Move one stone from cell (2,2) to cell (1,2).
3- Move one stone from cell (1,2) to cell (0,2).
In total, it takes 3 moves to place one stone in each cell of the grid.
It can be shown that 3 is the minimum number of moves required to place one stone in each cell.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2023/08/23/example2-2.svg" style="width: 401px; height: 281px;" />
<pre>
<strong>Input:</strong> grid = [[1,3,0],[1,0,0],[1,0,3]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> One possible sequence of moves to place one stone in each cell is:
1- Move one stone from cell (0,1) to cell (0,2).
2- Move one stone from cell (0,1) to cell (1,1).
3- Move one stone from cell (2,2) to cell (1,2).
4- Move one stone from cell (2,2) to cell (2,1).
In total, it takes 4 moves to place one stone in each cell of the grid.
It can be shown that 4 is the minimum number of moves required to place one stone in each cell.
</pre>

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

<ul>
	<li><code>grid.length == grid[i].length == 3</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 9</code></li>
	<li>Sum of <code>grid</code> is equal to <code>9</code>.</li>
</ul>

class Solution:
    def minimumMoves(self, grid: List[List[int]]) -> int:
        endState = (1, 1, 1, 1, 1, 1, 1, 1, 1)
        neighbors = [
            [1, 3], 
            [0, 2, 4], 
            [1, 5], 
            [0, 4, 6], 
            [1, 3, 5, 7], 
            [2, 4, 8], 
            [3, 7], 
            [4, 6, 8], 
            [5, 7]
        ]
        state = tuple(grid[0] + grid[1] + grid[2])

        def getNextStates(state):
            res = set()
            for i in range(9):
                if state[i] == 0:
                    for j in neighbors[i]:
                        if state[j] > 0:
                            nstate = list(state)
                            nstate[i], nstate[j] = 1, nstate[j] - 1
                            res.add(tuple(nstate))
            
            return res
        
        visited = set()
        q = {state}
        res = 0

        cnt = 0
        while q and cnt < 100:
            print(cnt, q)
            cnt += 1

            if endState in q:
                return res
            
            visited |= q
            nq = set()
            for s in q:
                nq |= getNextStates(s)
            

            nq -= visited
            q = nq
            res += 1
        
        return res

17000