<p>You are given a <strong>0-indexed</strong> <code>m x n</code> matrix <code>grid</code> consisting of <strong>positive</strong> integers.</p>

<p>You can start at <strong>any</strong> cell in the first column of the matrix, and traverse the grid in the following way:</p>

<ul>
	<li>From a cell <code>(row, col)</code>, you can move to any of the cells: <code>(row - 1, col + 1)</code>, <code>(row, col + 1)</code> and <code>(row + 1, col + 1)</code> such that the value of the cell you move to, should be <strong>strictly</strong> bigger than the value of the current cell.</li>
</ul>

<p>Return <em>the <strong>maximum</strong> number of <strong>moves</strong> that you can perform.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2023/04/11/yetgriddrawio-10.png" style="width: 201px; height: 201px;" />
<pre>
<strong>Input:</strong> grid = [[2,4,3,5],[5,4,9,3],[3,4,2,11],[10,9,13,15]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can start at the cell (0, 0) and make the following moves:
- (0, 0) -&gt; (0, 1).
- (0, 1) -&gt; (1, 2).
- (1, 2) -&gt; (2, 3).
It can be shown that it is the maximum number of moves that can be made.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<img alt="" src="https://assets.leetcode.com/uploads/2023/04/12/yetgrid4drawio.png" />
<strong>Input:</strong> grid = [[3,2,4],[2,1,9],[1,1,7]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Starting from any cell in the first column we cannot perform any moves.
</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>2 &lt;= m, n &lt;= 1000</code></li>
	<li><code>4 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution:
    def maxMoves(self, grid: List[List[int]]) -> int:
        def check(x,y):
            return 0 <= x < row_limit and 0<= y < col_limit and (x,y) not in visited
        def bfs(x,y):
            deq = deque([(x,y)])
            level = -1
            while deq:
                level += 1
                for _ in range(len(deq)):
                    x, y  = deq.popleft()
                    for dx, dy  in directions:
                        nxt_x = x + dx
                        nxt_y = y + dy
                        if check(nxt_x,nxt_y):
                            if grid[nxt_x][nxt_y] > grid[x][y]:
                                visited.add((nxt_x,nxt_y))
                                deq.append((nxt_x,nxt_y))
            # print(x,y,level)
            return level
            
        directions = [(-1,1),(0,1),(1,1)]
        ans = 0
        visited = set()

        row_limit = len(grid)
        col_limit = len(grid[0])
        
        for row in range(row_limit):
                moves = bfs(row,0)
                ans = max(moves,ans)
        
        return ans
948