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    # bfs\n    def numBusesToDestination(self, routes: List[List[int]], S: int, T: int) -> int:\n\n        md, que, visited, changes = collections.defaultdict(set), collections.deque(), set(), {}\n\n        # prre-processing, we can get dict m[1] = (0), m[2] = (0), m[7] = (0,1) ,etc\n        # means for stop 7 , bus 0, and 1 can reach\n        for b, r in enumerate(routes):\n            for s in r:\n                md[s].add(b)\n\n        # S or T not reachable\n        if S not in md or T not in md:\n            return -1\n\n        # if S and T are same, we don't even need to take bus\n        if S == T:\n            return 0\n\n        for b in md[S]:\n            for stop in routes[b]:\n                # (2,0,0), (7,0,0)\n                # (1,0,0) - means stop 1, bus 0, bus changes 0\n                que.append((stop, b, 1))\n                # changes[1,0] = 0, changes[2,0] = 0, changes[7,0] = 0\n                # means for reach 1,2,7 we just 1 times of bus change\n                # (take the first bus also count as 1 change)\n                changes[stop, b] = 1\n\n        while que:\n            stop, bus, times = que.popleft()\n            # already reach the Target\n            if stop == T:\n                return times\n            for b in md[stop]:\n                if bus != b:\n                    for stop in routes[b]:\n                        # if I already reached this stop by bus, but I used few times for change\n                        if (stop, bus) in changes and changes[stop, bus] > 1 + times:\n                            que.append((stop, bus, 1 + times))\n                            # remember update the new times in cache\n                            changes[stop, bus] = 1 + times\n                        elif (stop, bus) not in changes:  # I never reached stop by this bus yet\n                            changes[stop, bus] = 1 + times\n                            que.append((stop, bus, 1 + times))\n                        # else: if I reached stop by bus, but I changed more times than the record in cache,\n                        # just prunning it\n                    # this sentences improve the performance greatly\n                    # the time is from 5000ms decrease to 260 ms\n                    routes[b] = []\n\n        return -1\n\n    # dijkstra\n    def numBusesToDestination(self, routes: List[List[int]], S: int, T: int) -> int:\n\n        md, heap, visited, changes = collections.defaultdict(set), [], set(), set()\n\n        # prre-processing, we can get dict m[1] = (0), m[2] = (0), m[7] = (0,1) ,etc\n        # means for stop 7 , bus 0, and 1 can reach\n        for b, r in enumerate(routes):\n            for s in r:\n                md[s].add(b)\n\n        # S or T not reachable\n        if S not in md or T not in md:\n            return -1\n\n        # if S and T are same, we don't even need to take bus\n        if S == T:\n            return 0\n\n        for b in md[S]:\n            for stop in routes[b]:\n                # for test case: [[1,2,7],[3,6,7]], 1, 6\n                # we got (1,0,2), (1,0,7)\n                # means from stop 1 to go to stop 2 and 7, we just need to take one bus (1 changes )\n                heapq.heappush(heap, (1, b, stop))\n                # changes[1,0] = 0, changes[2,0] = 0, changes[7,0] = 0\n                # means for reach 1,2,7 we just 1 times of bus change\n                # (take the first bus also count as 1 change)\n                changes.add((stop, b))\n\n        while heap:\n            times, bus, stop = heapq.heappop(heap)\n            # already reach the Target\n            if stop == T:\n                return times\n            for b in md[stop]:\n                if bus != b:\n                    for stop in routes[b]:\n                        if (stop, bus) not in changes:  # I never reached stop by this bus yet\n                            changes.add((stop, bus))\n                            heapq.heappush(heap, (1 + times, bus, stop))\n        return -1\n\n    def numBusesToDestination(self, routes: List[List[int]], S: int, T: int) -> int:\n\n        if S == T:\n            return 0\n        graph = collections.defaultdict(set)\n\n        routes = list(map(set, routes))\n\n        for k1, r1 in enumerate(routes):\n            for k2 in range(k1 + 1, len(routes)):\n                if any(stop in routes[k2] for stop in r1):\n                    graph[k1].add(k2)\n                    graph[k2].add(k1)\n\n        seen, targets = set(), set()\n        for k, r in enumerate(routes):\n            if S in r:\n                seen.add(k)\n            if T in r:\n                targets.add(k)\n\n        que = [(node, 1) for node in seen]\n\n        while que:\n            node, depth = que.pop(0)\n            if node in targets:\n                return depth\n            for nei in graph[node]:\n                if nei not in seen:\n                    seen.add(nei)\n                    que.append((nei, depth + 1))\n\n        return -1\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: 8492