<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 {
public:

    int mod = 1e9+7;

    unordered_map<int, unordered_map<int, int>> mp;
    int solve(vector<vector<int>>& grid, int endx, int endy){
        if(mp.contains(endx) && mp[endx].contains(endy)){
            return mp[endx][endy];
        }
        int ret = 1;
        if(endx>0 && grid[endx-1][endy] < grid[endx][endy]){
            ret += solve(grid, endx-1, endy);
            ret %= mod;
        }
        if(endx<grid.size()-1 && grid[endx+1][endy] < grid[endx][endy]){
            ret += solve(grid, endx+1, endy);
            ret %= mod;
        }
        if(endy>0 && grid[endx][endy-1] < grid[endx][endy]){
            ret += solve(grid, endx, endy-1);
            ret %= mod;
        }
        if(endy<grid[0].size()-1 && grid[endx][endy+1] < grid[endx][endy]){
            ret += solve(grid, endx, endy+1);
            ret %= mod;
        }

        return mp[endx][endy]=ret;
    }
    int countPaths(vector<vector<int>>& grid) {

        int ret = 0;

        for(int i=0; i<grid.size(); i++){
            for(int j=0; j<grid[0].size(); j++){
                ret += solve(grid, i, j);
                ret %= mod;
            }
        }

        return ret;
    }
};
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