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    # O(n_stops x n_buses) time, O(n_stops x n_buses) space\n    def numBusesToDestination(self, routes: List[List[int]], S: int, T: int) -> int:\n        num_buses = len(routes)\n        bus_to_stop = defaultdict(set)\n        for bus, stops in enumerate(routes):\n            bus_to_stop[bus] = set(stops)\n        \n        def update_buses_used():\n            for bus in range(num_buses):\n                if bus in buses_used:\n                    continue\n                if stops_reached & bus_to_stop[bus]:\n                    buses_used.add(bus)\n        \n        def update_stops_reached():\n            for bus in buses_used:\n                stops_reached.update(bus_to_stop[bus])\n        \n        buses_used = set()\n        stops_reached = {S}\n        pre_stop_count = 0\n        bus_count = 0\n        while len(stops_reached) > pre_stop_count:\n            if T in stops_reached:\n                return bus_count\n            pre_stop_count = len(stops_reached)\n            update_buses_used()\n            update_stops_reached()\n            bus_count += 1\n            \n        return -1\n\n        \n    def numBusesToDestination(self, routes: List[List[int]], S: int, T: int) -> int:\n        stop_to_bus = defaultdict(set)\n        for bus, stops in enumerate(routes):\n            for stop in stops:\n                stop_to_bus[stop].add(bus)\n        \n        q = deque([(S, 0)])\n        seen = {S}\n        while q:\n            stop, bus_count = q.popleft()\n            if stop == T:\n                return bus_count\n            for bus in stop_to_bus[stop]:\n                for stop_new in routes[bus]:\n                    if stop_new in seen:\n                        continue\n                    seen.add(stop_new)\n                    q.append((stop_new, bus_count + 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: 8288