<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>

using ll = long long;
using pl = pair<ll, ll>;
using vl = vector<ll>;
using vvl = vector<vector<ll>>;
using vll = vector<pair<ll, ll>>;

#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

class Solution {
public:

const ll dx[4] = {-1,1,0,0};
const ll dy[4] = {0,0,-1,1};

ll dfs(ll x,ll y,ll n,ll m,vector<vector<int>> &a,vvl &dp){

    if(dp[x][y]!=-1)return dp[x][y]%((ll)1e9+7);
    
    ll res = 0; 
    for(ll k=0;k<4;k++){
        ll i = x+dx[k];ll j = y+dy[k];
        if(i>=0 and i<n and j>=0 and j<m){
           if(a[i][j]<a[x][y]){
              res+=dfs(i,j,n,m,a,dp);
           }
        }

    }

    
    dp[x][y] = (res+1)%((ll)(1e9+7));

    return dp[x][y];


}


int countPaths(vector<vector<int>>& a) {

    ll n = a.size(),m = a[0].size();
    ll mod = 1e9+7; vvl dp(n,vl(m,-1));ll flag =0;

    for(ll i=0;i<n;i++){
        for(ll j=0;j<m;j++){
            flag  = (flag+dfs(i,j,n,m,a,dp))%mod;
        }
    }
    

    return (int)flag%mod;

        
}


};
50733