<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>

int cmp(vector<int>&a, vector<int>&b){
    return a[0]<b[0];
}
class Solution {
public:
    int mod=1e9+7;
    int res=0;
    int dfs(int i, int j, vector<vector<int>>&grid,vector<vector<int>>&dp){
        // if(i==e1 && j==e2)return 1;
        int n=grid.size(),m=grid[0].size();
        if(dp[i][j]!=-1)return dp[i][j];
        int ans=1;
        if( i+1<n && grid[i+1][j]>grid[i][j]){
            ans=(ans+dfs(i+1,j,grid,dp))%mod;
            // vis[i+1][j]=1;
        }
        if(j+1<m && grid[i][j+1]>grid[i][j]){
            ans=(ans+dfs(i,j+1,grid,dp))%mod;
            // vis[i][j+1]=1;

        }
        if(i>0 &&grid[i-1][j]>grid[i][j]){
            ans=(ans+dfs(i-1,j,grid,dp))%mod;
            // vis[i-1][j]=1;

        }
        if(j>0 &&grid[i][j-1]>grid[i][j]){
            ans=(ans+dfs(i,j-1,grid,dp))%mod;
            // vis[i][j-1]=1;
        }
        res=(res+ans)%mod;
        return dp[i][j]=ans;
    }
    int countPaths(vector<vector<int>>& grid) {
        int n=grid.size(),m=grid[0].size();
        res=0;
        // int dp[n][m][n][m];
        vector<vector<int>>vis(n,vector<int>(m,-1));
        vector<vector<int>>temp;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                temp.push_back({grid[i][j],i,j});
            }
        }
        // sort(temp.begin(),temp.end(),cmp);
        for(auto it:temp){
            // if(vis[it[1]][it[2]]!=-1){
                // vis[it[1]][it[2]]=1;
                dfs(it[1],it[2],grid,vis);
            // }
            
        }
        return res;
    }
};
147441