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 = "from collections import defaultdict, deque\n\n\nclass Solution:\n    def numBusesToDestination(self, routes: List[List[int]], S: int, T: int) -> int:\n        '''\n        model as graph\n        find shortest path with BFS\n        \n        buses connect bus stops\n        \n        bus stops are vertices\n        \n        no\n        \n        routes are connected if they have a common point\n        \n        routes are vertices\n        \n        \n        '''\n        if S == T:\n            return 0\n        \n        g = Graph()\n        \n        sets = [set(route) for route in routes]\n        for s in sets:\n            if S in s and T in s:\n                return 1\n        \n        for i, s1 in enumerate(sets):\n            for j in range(i+1, len(sets)):\n                s2 = sets[j]\n                if not s1.isdisjoint(s2):\n                    g.connect(i, j)\n\n        starts = [i for i, s in enumerate(sets) if S in s]\n        ends = {i for i, s in enumerate(sets) if T in s}\n        min_steps = [g.min_steps(start, ends) for start in starts]\n        return min((x for x in min_steps if x > 0), default=-1)\n    \n\nclass Graph:\n    def __init__(self):\n        self.adj = defaultdict(set)\n        \n    def connect(self, p, q):\n        self.adj[p].add(q)\n        self.adj[q].add(p)\n        \n    def min_steps(self, start, ends):\n        seen = {start}\n        q = deque([start])\n        steps = 1\n        \n        while q:\n            for _ in range(len(q)):\n                p = q.popleft()\n                if p in ends:\n                    return steps\n                for v in self.adj[p]:\n                    if v in seen:\n                        continue\n                    seen.add(v)\n                    q.append(v)\n            \n            steps += 1\n        \n        return -1"
_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: 10320