<p>Given an <code>m x n</code> integers <code>matrix</code>, return <em>the length of the longest increasing path in </em><code>matrix</code>.</p>

<p>From each cell, you can either move in four directions: left, right, up, or down. You <strong>may not</strong> move <strong>diagonally</strong> or move <strong>outside the boundary</strong> (i.e., wrap-around is not allowed).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/05/grid1.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> matrix = [[9,9,4],[6,6,8],[2,1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest increasing path is <code>[1, 2, 6, 9]</code>.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/27/tmp-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> matrix = [[3,4,5],[3,2,6],[2,2,1]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>The longest increasing path is <code>[3, 4, 5, 6]</code>. Moving diagonally is not allowed.
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[1]]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= matrix[i][j] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution:
    def longestIncreasingPath(self, matrix: List[List[int]]) -> int:
        parents = defaultdict(set)
        adj = defaultdict(list)
        m = len(matrix)
        n = len(matrix[0])
        offs = [(0,1), (1,0), (0,-1), (-1,0)]
        for i1 in range(m):
            for j1 in range(n):
                for off_i, off_j in offs:
                    i2 = i1+off_i
                    j2 = j1+off_j
                    if 0<=i2<m and 0<=j2<n and matrix[i2][j2]>matrix[i1][j1]:
                        parents[(i2,j2)].add((i1,j1))
                        adj[(i1,j1)].append((i2,j2))
        # print(parents)
        q = deque([])
        for i in range(m):
            for j in range(n):
                node = (i,j)
                if len(parents[node])==0:
                    q.append(node)

        degree = defaultdict(lambda: 1)
        cur_degree = 0
        while q:
            new_q = deque([])
            while q:
                node = q.popleft()
                for neigh in adj[node]:
                    degree[neigh] = max(degree[neigh], 1+cur_degree)
                    parents[neigh].remove(node)
                    if len(parents[neigh])==0:
                        new_q.append(neigh)
            cur_degree += 1
            q = new_q

        return cur_degree
27045