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# # 以站点作为node建立graph，站点直接索引下一个站点: time limit exceeded... 怀疑是构建graph太耗时\n#         stop_graph = {}\n#         visited = set()\n#         for rt in routes:\n#             for i in range(len(rt)):\n#                 if rt[i] not in stop_graph: stop_graph[rt[i]] = set(rt[:i] + rt[i+1:])\n#                 else: \n#                     # print(rt[i], set(rt[:i] + rt[i+1:]))\n#                     stop_graph[rt[i]] = stop_graph[rt[i]].union(set(rt[:i] + rt[i+1:]))\n#         #BFS\n#         # visited = set()\n#         # print(stop_graph)\n#         if S == T: return 0\n#         if S not in stop_graph or T not in stop_graph: return -1\n#         cnt = 0\n#         queue = [S]\n#         visited = set(queue)\n#         while queue:\n#             # print(queue)\n#             size = len(queue)\n#             for _ in range(size):\n#                 curr_stop = queue.pop(0)\n#                 for next_stop in stop_graph[curr_stop]:\n#                     if next_stop in visited: continue\n#                     if next_stop == T: return cnt + 1\n#                     queue.append(next_stop) \n#                     visited.add(next_stop)\n#             cnt += 1\n#         else: return -1\n\n# 以站点作为node建立graph，但用站点索引bus班次，再用Bus索引站点的形式\n# ！！！避免time limit exceed方法必做事项：设两个set()分别记录遍历过的bust stop & bus route，每个stop / route都只应该最多坐一次，这样能避免重复便利stop/route带来的for循环耗时最终导致时间溢出\n        graph = {}\n        for i in range(len(routes)):\n            for st in routes[i]:\n                if st not in graph: graph[st] = [i]\n                else: graph[st].append(i)\n        \n        visited_st = set([S])\n        if S == T: return 0\n        if S not in graph or T not in graph: return -1\n        queue = graph[S]\n        # print(graph[S])\n        visited_rt = set(graph[S])\n        cnt = 0\n        while queue:\n            cnt += 1\n            size = len(queue)\n            for _ in range(size):\n                curr_rt_ind = queue.pop(0)\n                # if curr_rt_ind in visited: continue\n                # visited.add(curr_rt_ind)\n                for st in routes[curr_rt_ind]:\n                    if st in visited_st: continue\n                    if st == T: return cnt\n                    visited_st.add(st)\n                    for rt_ind in graph[st]:\n                        if rt_ind in visited_rt: continue\n                        queue.append(rt_ind)\n                        visited_rt.add(rt_ind)\n        else: return -1\n\n#         if S == T: return 0\n#         # routes = set(routes)\n#         graph = collections.defaultdict(set)\n#         for i, r1 in enumerate(routes):\n#             for j in range(i+1, len(routes)):\n#                 r2 = routes[j]\n#                 if any(r in r2 for r in r1):\n#                     graph[i].add(j)\n#                     graph[j].add(i)\n\n#         seen, targets = set(), set()\n#         for node, route in enumerate(routes):\n#             if S in route: seen.add(node)\n#             if T in route: targets.add(node)\n\n#         queue = [(node, 1) for node in seen]\n#         for node, depth in queue:\n#             if node in targets: return depth\n#             for nei in graph[node]:\n#                 if nei not in seen:\n#                     seen.add(nei)\n#                     queue.append((nei, depth+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: 6740