def expand(limit):
    lst = [0] * (limit + 1)
    for cur in range(2, limit + 1):
        simple = lst[cur - 1]
        root = int(cur ** 0.5)
        if root ** 2 == cur:
            simple = min(simple, lst[root])
        if not cur % 2:
            simple = min(simple, lst[cur // 2])
        for half in range(2, (cur + 1) // 2):
            simple = min(simple, lst[half] + lst[cur - half])
        lst[cur] = simple + 1
    return lst

print(expand(15))