from typing import List


def traverse_matrix(matrix: List[List[int]]) -> List[int]:
    n = len(matrix)
    def trav_rec(n, matrix):
        if n == 0:
            return []
        if n == 1:
            return [matrix[0][0]]
        if n == 2:
            return [matrix[0][0], matrix[0][1], matrix[1][1], matrix[1][0]]
        result = []
        result.extend(matrix[0])
        result.extend([matrix[i][-1] for i in range(1, n - 1)])
        result.extend(reversed(matrix[-1]))
        result.extend(reversed([matrix[i][0] for i in range(1, n-1)]))
        mini_matrix = [matrix[i][1:n-1] for i in range(1, n - 1)]
        result.extend(trav_rec(n - 2, mini_matrix))
        return result
    return trav_rec(n, matrix)