<p>You are given an <code>m x n</code> integer matrix <code>grid</code>, where you can move from a cell to any adjacent cell in all <code>4</code> directions.</p>

<p>Return <em>the number of <strong>strictly</strong> <strong>increasing</strong> paths in the grid such that you can start from <strong>any</strong> cell and end at <strong>any</strong> cell. </em>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>Two paths are considered different if they do not have exactly the same sequence of visited cells.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/10/griddrawio-4.png" style="width: 181px; height: 121px;" />
<pre>
<strong>Input:</strong> grid = [[1,1],[3,4]]
<strong>Output:</strong> 8
<strong>Explanation:</strong> The strictly increasing paths are:
- Paths with length 1: [1], [1], [3], [4].
- Paths with length 2: [1 -&gt; 3], [1 -&gt; 4], [3 -&gt; 4].
- Paths with length 3: [1 -&gt; 3 -&gt; 4].
The total number of paths is 4 + 3 + 1 = 8.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1],[2]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The strictly increasing paths are:
- Paths with length 1: [1], [2].
- Paths with length 2: [1 -&gt; 2].
The total number of paths is 2 + 1 = 3.
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 1000</code></li>
	<li><code>1 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>
</ul>

MOD = (10 ** 9) + 7
class Solution:
    def countPaths(self, grid: List[List[int]]) -> int:
        

        rows = len(grid)
        cols = len(grid[0])
        initial_spots = []

        dp = [[1] * cols for _ in range(rows)]


        required_visits = Counter()
        q = deque([])

        for r in range(rows):
            for c in range(cols):
                neighbors = [(1,0), (-1, 0), (0, 1), (0, -1)]

                smallest_local = True
                for dx, dy in neighbors:
                    r_n = r + dx
                    c_n = c + dy
            
                    if 0 <= r_n < rows and 0 <= c_n < cols:
                        if grid[r_n][c_n] < grid[r][c]:
                            smallest_local = False
                            required_visits[(r,c)] += 1
                
                if smallest_local:
                    q.append((r, c))

        s = 0
        visits = Counter()
        while q:
            neighbors = [(1,0), (-1, 0), (0, 1), (0, -1)]
            r, c = q.popleft()

            r_v = []

            for dx, dy in neighbors:
                r_n = r + dx
                c_n = c + dy
            
                if 0 <= r_n < rows and 0 <= c_n < cols:
                    if grid[r_n][c_n] > grid[r][c]:
                        dp[r_n][c_n] += dp[r][c] % MOD
                        dp[r_n][c_n] %= MOD
                        required_visits[(r_n, c_n)] -= 1

                        if required_visits[(r_n,c_n)] == 0:
                            q.append((r_n, c_n))

            s = (s + dp[r][c] % MOD) % MOD
        
        return s


        

                
        
42778