<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>

class Solution:
    def countPaths(self, matrix: List[List[int]]) -> int:
        ROWS, COLS = len(matrix),len(matrix[0])
        MODULO = 10**9 + 7
        def dp(r, c):
            count_path = 1
            if r < 0 or r >= ROWS or c < 0 or c >= COLS:
                return 1

            if (r, c) not in memo:
                if r-1 >= 0 and matrix[r][c] < matrix[r-1][c]:
                    count_path += dp(r-1, c)
                if r+1 < ROWS and matrix[r][c] < matrix[r+1][c]:
                    count_path += dp(r+1, c)
                if c+1 < COLS and matrix[r][c] < matrix[r][c+1]:
                    count_path += dp(r, c+1)
                if c-1 >= 0 and matrix[r][c] < matrix[r][c-1]:
                    count_path += dp(r, c-1)
                memo[(r, c)] = count_path
            return memo[(r, c)]
        memo = {}
        ans = 0
        for row in range(ROWS):
            for col in range(COLS):
               ans += dp(row, col)
        return ans % MODULO

1487