How to understand leetcode's word serach best solution in Python?

Question

I'm currently working on solving leetcode's word search task, and i see the fastest solution in Python is like this:

class Solution:
def exist(self, board: List[List[str]], word: str) -> bool:
    def backtracking(r,c,step=0):
        if step == len(word):return True
        if 0 <= r < m and 0 <= c < n and board[r][c] == word[~step] and (r,c) not in visited:
            visited.add((r,c))
            Hashmap[(r,c,step)] += 1
            for nr,nc in (r,c+1),(r,c-1),(r+1,c),(r-1,c):
                if Hashmap[(nr,nc,step+1)] < n:
                    if backtracking(nr,nc,step+1):
                        return True
            visited.remove((r,c))
            return False

    m,n = len(board),len(board[0])
    visited,Hashmap = set(),collections.defaultdict(int)
    for i,j in itertools.product(range(m),range(n)):
        if backtracking(i,j):
            return True
    return False

What confuses me most is how to understand the existence of [Hashmap] and the sentence

if Hashmap[(nr,nc,step+1)] < n:

how does it accelerate the progress?