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        \n        if S == T:\n            return 0\n        n = len(routes)\n        for i in range(n):\n            routes[i].sort()\n        graph = [[] for i in range(n)]\n        for i in range(n):\n            for j in range(i):\n                if self.haveCommonValues(routes[i], routes[j]):\n                    graph[i].append(j)\n                    graph[j].append(i)\n        print(graph)\n        targets = set()\n        vis = set()\n        for i in range(n):\n            if self.binary_search(routes[i], T):\n                targets.add(i)\n            if self.binary_search(routes[i], S):\n                vis.add(i)\n        print(vis)\n        print(targets)\n        step = 1\n        q = list(vis)\n        while q:\n            temp = []\n            for cur in q:\n                if cur in targets:\n                    return step\n                for nei in graph[cur]:\n                    if nei not in vis:\n                        vis.add(nei)\n                        temp.append(nei)\n            q = temp\n            step += 1\n        return -1\n                    \n    \n    def binary_search(self, A, target):\n        l = 0\n        r = len(A) - 1\n        while l <= r:\n            mid = (l+r)//2\n            if A[mid]==target:\n                return True\n            if target < A[mid]:\n                r = mid - 1\n            else:\n                l = mid + 1\n        return False\n                \n    \n    def haveCommonValues(self, A, B):\n    \n        i = 0\n        j = 0\n        while i < len(A):\n            while j < len(B) and B[j] < A[i]:\n                j += 1\n            if j == len(B):\n                return False\n            if B[j] == A[i]:\n                return True\n            i += 1\n        return False'
_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: 8077