<p>On an <code>2 x 3</code> board, there are five tiles labeled from <code>1</code> to <code>5</code>, and an empty square represented by <code>0</code>. A <strong>move</strong> consists of choosing <code>0</code> and a 4-directionally adjacent number and swapping it.</p>

<p>The state of the board is solved if and only if the board is <code>[[1,2,3],[4,5,0]]</code>.</p>

<p>Given the puzzle board <code>board</code>, return <em>the least number of moves required so that the state of the board is solved</em>. If it is impossible for the state of the board to be solved, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide1-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[1,2,3],[4,0,5]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> Swap the 0 and the 5 in one move.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide2-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[1,2,3],[5,4,0]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> No number of moves will make the board solved.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide3-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[4,1,2],[5,0,3]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> 5 is the smallest number of moves that solves the board.
An example path:
After move 0: [[4,1,2],[5,0,3]]
After move 1: [[4,1,2],[0,5,3]]
After move 2: [[0,1,2],[4,5,3]]
After move 3: [[1,0,2],[4,5,3]]
After move 4: [[1,2,0],[4,5,3]]
After move 5: [[1,2,3],[4,5,0]]
</pre>

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

<ul>
	<li><code>board.length == 2</code></li>
	<li><code>board[i].length == 3</code></li>
	<li><code>0 &lt;= board[i][j] &lt;= 5</code></li>
	<li>Each value <code>board[i][j]</code> is <strong>unique</strong>.</li>
</ul>

class Solution {
public:
    int slidingPuzzle(vector<vector<int>>& board) 
    {
        set<vector<vector<int>>>vis;
        int cnt = 0;
        vector<vector<int>>ans = {{1,2,3},{4,5,0}};
        if(board == ans)
            return cnt;
        queue< pair<vector<vector<int>>,vector<int>> >qu;
        int x,y;
        for(int i = 0;i<2;i++){
        for(int j = 0;j<3;j++) if(board[i][j] == 0) x= i,y=j;}
        qu.push({board,{x,y}});
        while(!qu.empty())
        {
            int sz = qu.size();
            while(sz--)
            {
                vector<vector<int>>out = qu.front().first;
                vis.insert(out);
                if(out == ans)
                    return cnt;
                x = qu.front().second[0], y = qu.front().second[1];
                qu.pop();
                if(x+1 < 2)
                {
                    swap(out[x+1][y],out[x][y]);
                    if(vis.find(out) == vis.end())
                        qu.push({out,{x+1,y}});
                    swap(out[x+1][y],out[x][y]);
                }
                if(x-1 >= 0)
                {
                    swap(out[x-1][y],out[x][y]);
                    if(vis.find(out) == vis.end())
                        qu.push({out,{x-1,y}});
                    swap(out[x-1][y],out[x][y]);
                }
                if(y+1 < 3)
                {
                    swap(out[x][y+1],out[x][y]);
                    if(vis.find(out) == vis.end())
                        qu.push({out,{x,y+1}});
                    swap(out[x][y+1],out[x][y]);
                }
                if(y-1 >= 0)
                {
                    swap(out[x][y-1],out[x][y]);
                    if(vis.find(out) == vis.end())
                        qu.push({out,{x,y-1}});
                    swap(out[x][y-1],out[x][y]);
                }
            }
            cnt++;
        }
        return -1;
    }
};
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