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        for i in range(len(routes)):\n            routes[i] = set(routes[i])\n        \n        start_bus = set()\n        end_bus = set()\n        connections = collections.defaultdict(set)\n        for i in range(len(routes)):\n            busA = routes[i]\n            \n            if S in busA:\n                start_bus.add(i)\n                \n            if T in busA:\n                end_bus.add(i)\n            \n            for j in range(len(routes)):\n                if i == j:\n                    continue\n                    \n                busB = routes[j]\n                if len(busA & busB):\n                    connections[i].add(j)\n                   \n        if start_bus == end_bus:\n            return 1 if S != T else 0\n\n        S = list(start_bus)[0]\n        T = list(end_bus)[0]\n                    \n        # print(start_bus, end_bus, connections)\n        \n        # connections = collections.defaultdict(set)\n        # for r in routes:\n        #     for i in range(len(r)):\n        #         for j in range(len(r)):\n        #             if i != j:\n        #                 connections[r[i]].add(r[j])\n\n        first_hop = 1\n        # q = [(first_hop, S)]\n        \n        q = [(1, s) for s in start_bus]\n        \n        seen = set()\n\n        ans = float('inf')\n        while q:\n            # print(q)\n            W, C = heapq.heappop(q)\n            \n            if C in end_bus:\n                end_bus.remove(C)\n                \n                ans = min(ans, W)\n                \n                if not end_bus:\n                    break\n            \n            if C in seen:\n                continue\n\n            seen.add(C)\n\n            W += 1\n            for i in connections[C]:\n                if i not in seen:\n                    heapq.heappush(q, (W, i))\n        \n        return -1 if ans == float('inf') else ans\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: 8480