We have a list of bus routes. Each routes[i] is a bus route that the i-th bus repeats forever. For example if routes[0] = [1, 5, 7], this means that the first bus (0-th indexed) travels in the sequence 1->5->7->1->5->7->1->... forever.
We start at bus stop S (initially not on a bus), and we want to go to bus stop T. Travelling by buses only, what is the least number of buses we must take to reach our destination? Return -1 if it is not possible.
Example:
Input: 
routes = [[1, 2, 7], [3, 6, 7]]
S = 1
T = 6
Output: 2
Explanation: 
The best strategy is take the first bus to the bus stop 7, then take the second bus to the bus stop 6.

 
Constraints:

1 <= routes.length <= 500.
1 <= routes[i].length <= 10^5.
0 <= routes[i][j] < 10 ^ 6.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'class Solution:\n    def numBusesToDestination(self, bus_routes: List[List[int]], start: int, end: int) -> int:\n        # return self.approach_2(bus_routes, start, end)\n        if start == end:\n            return 0\n        on_stop = defaultdict(set)\n        for i, route in enumerate(bus_routes):\n            for stop in route:\n                on_stop[stop].add(i)\n        bfs = []\n        bfs.append((start, 0))\n        seen = set([start])\n        for stop, bus_count in bfs:\n            if stop == end:\n                return bus_count\n            for buses in on_stop[stop]:\n                for stops in bus_routes[buses]:\n                    if stops not in seen:\n                        if stops == end:\n                            return bus_count+1\n                        seen.add(stops)\n                        bfs.append((stops, bus_count+1))\n                bus_routes[buses] = []\n        return -1\n\n    def approach_2(self, bus_routes, start, end):\n        if start == end: return 0\n        graph = defaultdict(set)\n        bus_routes = list(map(set, bus_routes))\n        start_set = set()\n        end_set = set()\n        for bus, stops in enumerate(bus_routes):\n            for other_buses in range(bus+1, len(bus_routes)):\n                other_bus_route = bus_routes[other_buses]\n                if not other_bus_route.isdisjoint(stops):\n                    graph[bus].add(other_buses)\n                    graph[other_buses].add(bus)\n        for bus,route in enumerate(bus_routes):\n            if start in route: start_set.add(bus)\n            if end in route: end_set.add(bus)\n\n        queue = [(node, 1) for node in start_set]\n        for bus, changes in queue:\n            if bus in end_set: return changes\n            for nei in graph[bus]:\n                if nei not in start_set:\n                    start_set.add(nei)\n                    queue.append((nei, changes+1))\n        return -1\n    \n    def approach_3(self, buses, start, end):\n        on_stop = defaultdict(set)\n        for bus, stops in enumerate(buses):\n            for stop in stops:\n                on_stop[stop].add(bus)\n        bfs = [(start, 0)]\n        seen = set()\n        seen.add(start)\n        for stop, dist in bfs:\n            if stop == end:\n                return dist\n            for bus in on_stop[stop]:\n                for stops in buses[bus]:\n                    if end == start:\n                        return dist+1\n                    if stops not in seen:\n                        seen.add(stops)\n                        bfs.append((stops, dist+1))\n        return -1\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'numBusesToDestination'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 7344