<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;
    int dp[1001][1001];
    int helper(vector<vector<int>>& grid,int &x,int &y){
        if(dp[x][y]!=-1){
            return dp[x][y];
        }
        int m=grid.size();
        int n=grid[0].size();
        long long count=1;
        vector<pair<int,int>> dir{{0,1},{0,-1},{1,0},{-1,0}};
        for(int i=0;i<dir.size();i++){
            int n_x=x+dir[i].first;
            int n_y=y+dir[i].second;
            if(n_x>=0 && n_x<m && n_y>=0 && n_y<n && grid[n_x][n_y]>grid[x][y]){
                count+=helper(grid,n_x,n_y);
            }
        }
        dp[x][y]=count%mod;
        return dp[x][y];
    }
    int countPaths(vector<vector<int>>& grid) {
        int m=grid.size();
        int n=grid[0].size();
        // vector<vector<int>> dp(m,vector<int>(n,-1));
        memset(dp, -1, sizeof(dp));
        long long count=0;
        for(int i=0;i<m;i++){
            for(int j=0;j<n;j++){
                count+=helper(grid,i,j);
            }
        }
        return count%mod;
    }
};
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