Search a path with increasing value given two nodes

Search a path with increasing value given two nodes in matrix

Problem statement:
you are given a matrix. Size m rows, n columns. start point and end point.
try to find a path from start point to end point, in the path, the next value is bigger then the previous value.
Every time you can go four directions, left, top, right and bottom. 

For example, 
[[1,4,5,3]
 [2,4,0,1]
 [3,6,8,-1]]
 
start = [0,0]  end [2,2]

==> [0,0], [1,0], [2,0],[2,1], [2,2]
      1       2     3     6      8
      
Julia's analysis:

      rows * columns -> length of path 
      visit - mark visit
      DFS/ BFS -> exhaust all options 
      constraint: next step is bigger than current
      shortest path -> no confliction
      BFS -> node 1, at most four neighbors -> add neighbors > 1 to queue, mark 1 is visted, prefix 1->
      
Here is my idea to write a solution:

      //int layerIndex = 0;
      while(queue.count > 0 )
      {               
          countOfqueue = queue.count; // 
          deque one by one 
          {
          // check four possible neighbor, unvisited before, see bigger than previous neighbor -> check prefix
          if(desitinatian node = )
            return path = prefix + add current neighbornode            
          }
          else {
          add those node to queuue
          }          
      }