<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:
    using ll = long long;
    const int mod = 1e9+7;
    int countPaths(vector<vector<int>>& g) {
        vector<pair<int,int>> mvs = {{-1,0},{1,0},{0,1},{0,-1}};
        int n = g.size(),m = g[0].size();
        auto isvalid = [&](int x,int y)->bool{
            return x>=0 && x<n && y>=0 && y<m ; 
        };
        vector<vector<ll>> dp(n,vector<ll>(m));
        vector<vector<bool>> vis(n,vector<bool>(m));
        ll ans = 0;
        function<void(int,int)> dfs = [&](int x,int y){
            dp[x][y] = 1;
            vis[x][y] = true;
            for(auto [dx,dy]:mvs) {
                int xd = x + dx,yd = y + dy;
                if(isvalid(xd,yd) && g[xd][yd] > g[x][y]){
                    if(!vis[xd][yd])
                    dfs(xd,yd);
                    (dp[x][y] += dp[xd][yd])%=mod; 
                }
            }
            // cout<<x<<" "<<y<<" "<<dp[x][y]<<endl;
            (ans += dp[x][y])%=mod;
        };
        for(int i=0;i<n;i++) for(int j=0;j<m;j++) if(!dp[i][j]) dfs(i,j);
        return (int)ans;
        
    }
};
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