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, routes: List[List[int]], S: int, T: int) -> int:\n#         # This is a very good BFS problem.\n#     # In BFS, we need to traverse all positions in each level firstly, and then go to the next level.\n#     # Our task is to figure out:\n#     # 1. What is the level in this problem?\n#     # 2. What is the position we want in this problem?\n#     # 3. How to traverse all positions in a level?\n#     # \n#     # For this problem:\n#     # 1. The level is each time to take bus.\n#     # 2. The position is all of the stops you can reach for taking one time of bus.\n#     # 3. Using a queue to record all of the stops can be arrived for each time you take buses.\n#         \\"\\"\\"\n#         :type routes: List[List[int]]\n#         :type S: int\n#         :type T: int\n#         :rtype: int\n#         \\"\\"\\"\n#         # You already at the terminal, so you needn\'t take any bus.\n#         if S == T: return 0\n        \n#         # You need to record all the buses you can take at each stop so that you can find out all\n#         # of the stops you can reach when you take one time of bus.\n#         # the key is stop and the value is all of the buses you can take at this stop.\n#         stopBoard = {} \n#         for bus, stops in enumerate(routes):\n#             for stop in stops:\n#                 if stop not in stopBoard:\n#                     stopBoard[stop] = [bus]\n#                 else:\n#                     stopBoard[stop].append(bus)\n#         print(stopBoard)\n#         # The queue is to record all of the stops you can reach when you take one time of bus.\n#         queue = deque([S])\n#         # Using visited to record the buses that have been taken before, because you needn\'t to take them again.\n#         visited = set()\n\n#         res = 0\n#         while queue:\n#             # take one time of bus.\n#             res += 1\n#             # In order to traverse all of the stops you can reach for this time, you have to traverse\n#             # all of the stops you can reach in last time.\n#             for _ in range(len(queue)):\n#                 curStop = queue.popleft()\n#                 # Each stop you can take at least one bus, you need to traverse all of the buses at this stop\n#                 # in order to get all of the stops can be reach at this time.\n#                 for bus in stopBoard[curStop]:\n#                     # if the bus you have taken before, you needn\'t take it again.\n#                     if bus in visited: continue\n#                     visited.add(bus)\n#                     for stop in routes[bus]:\n#                         if stop == T: return res\n#                         queue.append(stop)\n#         return -1\n\n    def numBusesToDestination(self, routes, S, T):\n        to_routes = collections.defaultdict(set)\n        for i, route in enumerate(routes):\n            for j in route:\n                to_routes[j].add(i)\n        bfs = collections.deque([(S, 0)])\n        seen = set([S])\n        while bfs:\n            for _ in range(len(bfs)):\n                stop, bus = bfs.popleft()\n                if stop == T: \n                    return bus\n                for i in to_routes[stop]:\n                    for j in routes[i]:\n                        if j in seen:\n                            continue\n                        bfs.append((j, bus + 1))\n                        seen.add(j)\n        return -1\n\n\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: 8488