input: Write a function named `connect_and_query_databases` that connects to MySQL, MongoDB, and PostgreSQL databases, executes a query on each, and returns the results as a dictionary. The function should use the `pymysql`, `MongoClient` from `pymongo`, and `psycopg2` libraries. If any connection or query fails, the function should return `None`.
  assert connect_and_query_databases() == {
      'mysql': ['data1', 'data2'],
      'mongodb': ['data3', 'data4'],
      'postgresql': ['data5', 'data6']
  }
  assert connect_and_query_databases() == None # if connection or query fails
output: def connect_and_query_databases():
      try:
          import pymysql
          from pymongo import MongoClient
          import psycopg2
          
          # MySQL connection and query
          mysql_conn = pymysql.connect(host='localhost', user='root', password='password', db='test')
          mysql_cursor = mysql_conn.cursor()
          mysql_cursor.execute("SELECT * FROM test_table")
          mysql_result = [row[0] for row in mysql_cursor.fetchall()]
          mysql_conn.close()
          
          # MongoDB connection and query
          mongo_client = MongoClient('localhost', 27017)
          mongo_db = mongo_client['test_db']
          mongo_collection = mongo_db['test_collection']
          mongo_result = [doc['data'] for doc in mongo_collection.find()]
          mongo_client.close()
          
          # PostgreSQL connection and query
          pg_conn = psycopg2.connect(host='localhost', dbname='test_db', user='postgres', password='password')
          pg_cursor = pg_conn.cursor()
          pg_cursor.execute("SELECT * FROM test_table")
          pg_result = [row[0] for row in pg_cursor.fetchall()]
          pg_conn.close()
          
          return {
              'mysql': mysql_result,
              'mongodb': mongo_result,
              'postgresql': pg_result
          }
      except:
          return None