# Python >= 3.9
def square(n: int) -> list[list[float]]:
    from itertools import permutations
    from random import random
    
    matrix = [list([0]*n) for _ in range(n)]
    total  = 0.0
    for index in permutations(range(n)):
        value = random()
        total += value
        for i, j in enumerate(index):
            matrix[i][j] += value
    return [[elem / total for elem in row] for row in matrix]