from typing import List

def count_islands(matrix: List[List[int]]) -> int:

if not matrix:

return 0

count = 0

for r in range(len(matrix)):

for c in range(len(matrix[0])):

# If a land cell is found, perform DFS to explore the full

# island, and include this island in our count.

if matrix[r][c] == 1:

dfs(r, c, matrix)

count += 1

return count

def dfs(r: int, c: int, matrix: List[List[int]]) -> None:

# Mark the current land cell as visited.

matrix[r][c] = -1

# Define direction vectors for up, down, left, and right.

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

# Recursively call DFS on each neighboring land cell to continue

# exploring this island.

for d in dirs:

next_r, next_c = r + d[0], c + d[1]

if is_within_bounds(next_r, next_c, matrix) and matrix[next_r][next_c] == 1:

dfs(next_r, next_c, matrix)

def is_within_bounds(r: int, c: int, matrix: List[List[int]]) -> bool:

return 0 <= r < len(matrix) and 0 <= c < len(matrix[0])