<p>You are asked to cut off all the trees in a forest for a golf event. The forest is represented as an <code>m x n</code> matrix. In this matrix:</p>

<ul>
	<li><code>0</code> means the cell cannot be walked through.</li>
	<li><code>1</code> represents an empty cell that can be walked through.</li>
	<li>A number greater than <code>1</code> represents a tree in a cell that can be walked through, and this number is the tree&#39;s height.</li>
</ul>

<p>In one step, you can walk in any of the four directions: north, east, south, and west. If you are standing in a cell with a tree, you can choose whether to cut it off.</p>

<p>You must cut off the trees in order from shortest to tallest. When you cut off a tree, the value at its cell becomes <code>1</code> (an empty cell).</p>

<p>Starting from the point <code>(0, 0)</code>, return <em>the minimum steps you need to walk to cut off all the trees</em>. If you cannot cut off all the trees, return <code>-1</code>.</p>

<p><strong>Note:</strong> The input is generated such that no two trees have the same height, and there is at least one tree needs to be cut off.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/trees1.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> forest = [[1,2,3],[0,0,4],[7,6,5]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> Following the path above allows you to cut off the trees from shortest to tallest in 6 steps.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/trees2.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> forest = [[1,2,3],[0,0,0],[7,6,5]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> The trees in the bottom row cannot be accessed as the middle row is blocked.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> forest = [[2,3,4],[0,0,5],[8,7,6]]
<strong>Output:</strong> 6
<b>Explanation:</b> You can follow the same path as Example 1 to cut off all the trees.
Note that you can cut off the first tree at (0, 0) before making any steps.
</pre>

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

<ul>
	<li><code>m == forest.length</code></li>
	<li><code>n == forest[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>0 &lt;= forest[i][j] &lt;= 10<sup>9</sup></code></li>
	<li>Heights of all trees are <strong>distinct</strong>.</li>
</ul>

class Solution:
    def cutOffTree(self, forest: List[List[int]]) -> int:
        def bfs(i, j, x, y):
            queue = deque()
            queue.append((i, j, 0))
            been = set()
            been.add((i, j))
            while queue:
                curr_x, curr_y, steps = queue.popleft()
                if curr_x == x and curr_y == y:
                    return steps
                for next_x, next_y in [(curr_x + 1, curr_y), (curr_x - 1, curr_y), (curr_x, curr_y + 1), (curr_x, curr_y - 1)]:
                    if 0 <= next_x < len(forest) and 0 <= next_y < len(forest[0]) and forest[next_x][next_y] > 0 and (next_x, next_y) not in been:
                        queue.append((next_x, next_y, steps + 1))
                        been.add((next_x, next_y))
            return -1        
        
        if forest[0][0] == 0:
            return -1
        pq = []
        for x in range(len(forest)):
            for y in range(len(forest[0])):
                if forest[x][y] > 1:
                    heapq.heappush(pq, (forest[x][y], x, y))
        cx, cy = 0, 0
        res = 0
        while pq:
            tree, nx, ny = heapq.heappop(pq)
            s =  bfs(cx, cy, nx, ny)
            if s >= 0:
                res += s
                forest[nx][ny] = 1
                cx, cy = nx, ny
            else:
                return -1
        return res
17100