<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 countPaths(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        int mod = 1e9+7;

        map<pair<int,int>,int>map1;
        vector<pair<int,pair<int,int>>> v1;
        for(int i = 0; i<n; i++)
        {
            for(int j = 0; j<m; j++)
            {
                v1.push_back({grid[i][j],{i,j}});
            }
        }
        sort(v1.rbegin(),v1.rend());

        int delx[] = {-1,0,1,0};
        int dely[] = {0,1,0,-1};

        long long ans = 0;

        for(int i = 0; i<n*m; i++)
        {
            int row = v1[i].second.first;
            int col = v1[i].second.second;

            long long sum = 0;
            for(int j = 0; j<4; j++)
            {
                int nrow = row+delx[j];
                int ncol = col+dely[j];

                if(nrow >= 0 && ncol >= 0 && nrow < n && ncol < m && grid[nrow][ncol] > grid[row][col])
                {
                    sum += map1[{nrow,ncol}];
                    sum %= mod;
                }
            }
            sum++;
            sum %= mod;
            ans += sum;
            ans %= mod;
            map1[{row,col}] = sum;
        }
        return ans;
    }
};
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