input: Write a python function to parse and encode OSM (OpenStreetMap) XML data into binary format. Use the `BinaryOsm` class provided in the code. Make sure the function handles nodes, ways, and tags correctly.
  
  ```python
  def test_binary_osm():
      binary_osm = BinaryOsm()
      
      # Test with a sample input file and output file.
      input_file = "sample_input.osm"
      output_file = "sample_output.bin"
      binary_osm.encode(input_file, output_file)
      
      # You can add more specific assertions based on the expected binary output if you have predefined expected outputs
      assert os.path.exists(output_file)
      
      # Additional tests for handling of nodes, ways, and tags
      sample_attrs_node = {'id': '1', 'lat': '10.0', 'lon': '20.0'}
      sample_attrs_way = {'id': '2'}
      sample_attrs_tag = {'k': 'name', 'v': 'Main Street'}
      
      binary_osm.startElement('node', sample_attrs_node)
      assert binary_osm.meta['id'] == 1
      assert binary_osm.meta['lat'] == 10.0
      assert binary_osm.meta['lon'] == 20.0
      
      binary_osm.startElement('way', sample_attrs_way)
      assert binary_osm.meta['id'] == 2
      
      binary_osm.startElement('tag', sample_attrs_tag)
      assert binary_osm.tags['name'] == 'Main Street'
  
  test_binary_osm()
output: def parse_and_encode_osm(input_file: str, output_file: str):
      import xml.sax
      import struct
      import os
  
      class BinaryOsm(xml.sax.ContentHandler):
          def __init__(self):
              self.meta = {}
              self.tags = {}
              self.nodes = []
              self.ways = []
  
          def startElement(self, name, attrs):
              if name == 'node':
                  self.meta = {
                      'id': int(attrs['id']),
                      'lat': float(attrs['lat']),
                      'lon': float(attrs['lon'])
                  }
              elif name == 'way':
                  self.meta = {'id': int(attrs['id'])}
              elif name == 'tag':
                  self.tags[attrs['k']] = attrs['v']
  
          def endElement(self, name):
              if name == 'node':
                  self.nodes.append((self.meta, self.tags))
                  self.meta = {}
                  self.tags = {}
              elif name == 'way':
                  self.ways.append((self.meta, self.tags))
                  self.meta = {}
                  self.tags = {}
  
          def encode(self, input_file, output_file):
              parser = xml.sax.make_parser()
              parser.setContentHandler(self)
              parser.parse(input_file)
  
              with open(output_file, 'wb') as f:
                  for node in self.nodes:
                      meta, tags = node
                      f.write(struct.pack('i', meta['id']))
                      f.write(struct.pack('d', meta['lat']))
                      f.write(struct.pack('d', meta['lon']))
                      for k, v in tags.items():
                          f.write(struct.pack('i', len(k)))
                          f.write(k.encode('utf-8'))
                          f.write(struct.pack('i', len(v)))
                          f.write(v.encode('utf-8'))
  
                  for way in self.ways:
                      meta, tags = way
                      f.write(struct.pack('i', meta['id']))
                      for k, v in tags.items():
                          f.write(struct.pack('i', len(k)))
                          f.write(k.encode('utf-8'))
                          f.write(struct.pack('i', len(v)))
                          f.write(v.encode('utf-8'))
  
      binary_osm = BinaryOsm()
      binary_osm.encode(input_file, output_file)