<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:
    bool valid(long long x,long long y,long long n,long long m){
        if(x>=0&&y>=0&&x<n&&y<m)return true;
        return false;
    }
    void dfs(long long x,long long y, vector<vector<int>>& k,vector<vector<bool>>& vis,vector<vector<long long>>& dp,long long n,long long m){
        vis[x][y]=true;
        long long M=1e9+7;
        if(dp[x][y]!=-1)return ;
        long long val=0;
        for(long long i=-1;i<=1;i++){
            for(long long j=-1;j<=1;j++){
                if(abs(i)==abs(j))continue;
                if(valid(x+i,y+j,n,m)&&k[x+i][y+j]>k[x][y]){
                    if(dp[x+i][y+j]==-1)dfs(x+i,y+j,k,vis,dp,n,m);
                    val+=dp[x+i][y+j]+1;
                    val=val%M;
                }
            }
        }
        dp[x][y]=val%M;
    }
    int countPaths(vector<vector<int>>& k) {
        long long n=k.size();
        long long m=k[0].size();
        vector<vector<bool>>vis(n,vector<bool>(m,false));
        vector<vector<long long>>dp(n,vector<long long>(m,-1));
        for(long long i=0;i<n;i++){
            for(long long j=0;j<m;j++){
                if(!vis[i][j]){
                    dfs(i,j,k,vis,dp,n,m);
                }
            }
        }long long ans=n*m;
        long long M=1e9+7;ans=ans%M;
        for(long long i=0;i<n;i++){
            for(long long j=0;j<m;j++){
                
                ans=ans+(long long)dp[i][j];
                ans=ans%M;
            }
        }return ans;
        
    }
};
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