def euler_122():
    upper = 201
    m_k = {k: 0 for k in range(2, upper)}
    sets = [[1]]
    for _ in range(11):
        new_sets = []
        for s in sets:
            for i in range(len(s)):
                new_elem = s[i] + s[-1]
                if new_elem in m_k and m_k[new_elem] == 0:
                    m_k[new_elem] = len(s)
                new_sets.append(s + [new_elem])

        # For better performance, we would have to prune here.
        sets = new_sets

    r = 0
    for k in range(2, upper):
        assert m_k[k] != 0
        r += m_k[k]
    return r


if __name__ == "__main__":
    solution = euler_122()
    print("e122.py: " + str(solution))
    assert solution == 1582