Translate the following question to SQL: What are the names of all of Alice's friends of friends?

Schema: CREATE TABLE Person (
    name varchar(20)   PRIMARY KEY,
    age INTEGER,
    city TEXT,
    gender TEXT,
    job TEXT,
    UNIQUE (name)
);

CREATE TABLE PersonFriend (
    name varchar(20),
    friend varchar(20),
    year INTEGER,
    FOREIGN KEY (friend) REFERENCES Person(name),
    FOREIGN KEY (name) REFERENCES Person(name)
);
user
SELECT DISTINCT T4.name FROM PersonFriend AS T1 JOIN Person AS T2 ON T1.name  =  T2.name JOIN PersonFriend AS T3 ON T1.friend  =  T3.name JOIN PersonFriend AS T4 ON T3.friend  =  T4.name WHERE T2.name  =  'Alice' AND T4.name != 'Alice'
assistant