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from collections import deque

# initialize variables
matrix = [row[:] for row in mat]
rows = len(matrix)
cols = len(matrix[0])
q = deque()
seen = set()

# initialize queue
for row in range(rows):
    for col in range(cols):
        if matrix[row][col] == 0:
            q.append((row, col, 0))
            seen.add((row, col))

directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]

# perform bfs
while q:
		# pop next node
    row, col, steps = q.popleft()
    
    # traverse neighbors
    for dx, dy in directions:
        next_row, next_col = row + dy, col + dx
        
        # perform logic
        if (next_row, next_col) not in seen and valid(next_row, next_col):
            seen.add((next_row, next_col))
            q.append((next_row, next_col, steps + 1))
            matrix[next_row][next_col] = steps + 1

return matrix