<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:
        if forest[0][0] == 0 :
            return -1
        m = len(forest)
        n = len(forest[0])
        def distance(node1, node2):
            now = [node1]
            soon = []
            expanded = set()
            manhattan = abs(node1[0] - node2[0]) + abs(node1[1] - node2[1])
            detours = 0
            while True:
                if len(now) == 0:
                    now = soon
                    soon = []
                    detours += 1
                node = now.pop()
                if node == node2:
                    return manhattan + 2 * detours
                if node not in expanded:
                    expanded.add(node)
                    x, y = node
                    if x - 1 >= 0 and forest[x - 1][y] >= 1:
                        if x > node2[0]:
                            now.append((x - 1, y))
                        else:
                            soon.append((x - 1, y))
                    if y + 1 < n and forest[x][y + 1] >= 1:
                        if y < node2[1]:
                            now.append((x, y + 1))
                        else:
                            soon.append((x, y + 1))
                    if x + 1 < m and forest[x + 1][y] >= 1:
                        if x < node2[0]:
                            now.append((x + 1, y))
                        else:
                            soon.append((x + 1, y))
                    if y - 1 >= 0 and forest[x][y - 1] >= 1:
                        if y > node2[1]:
                            now.append((x, y - 1))
                        else:
                            soon.append((x, y - 1))
        trees = []
        for i in range(m):
            for j in range(n):
                if forest[i][j] > 1:
                    trees.append(((i, j), forest[i][j]))
        trees.sort(key=lambda x: x[1])
        can_reach = {(0, 0)}
        stack = [(0, 0)]
        while len(stack) > 0:
            x, y = stack.pop()
            if x - 1 >= 0 and forest[x - 1][y] >= 1 and (x - 1, y) not in can_reach:
                can_reach.add((x - 1, y))
                stack.append((x - 1, y))
            if y + 1 < n and forest[x][y + 1] >= 1 and (x, y + 1) not in can_reach:
                can_reach.add((x, y + 1))
                stack.append((x, y + 1))
            if x + 1 < m and forest[x + 1][y] >= 1 and (x + 1, y) not in can_reach:
                can_reach.add((x + 1, y))
                stack.append((x + 1, y))
            if y - 1 >= 0  and forest[x][y - 1] >= 1 and (x, y - 1) not in can_reach:
                can_reach.add((x, y - 1))
                stack.append((x, y - 1))
        for t in trees:
            if t[0] not in can_reach:
                return -1
        start = (0, 0)
        num_step = 0
        for t in trees: 
            num_step += distance(start, t[0])
            forest[t[0][0]][t[0][1]] = 1
            start = t[0]
        return num_step
17800