In graph theory, a graph is a collection of nodes with connections between them.
Any node can be connected to any other node exactly once, and can be connected to no nodes, to some nodes, or to every other node.
Nodes cannot be connected to themselves
A path through a graph is a sequence of nodes, with every node connected to the node following and preceding it.
A closed path is a path which starts and ends at the same node.

An open path:
```
1 -> 2 -> 3
```
a closed path:
```
1 -> 2 -> 3 -> 1
```
A graph is connected if there is a path from every node to every other node.
A graph is a tree if it is connected and there are no closed paths.


Your job is to write a function 'isTree', which returns true if a graph is a tree, and false if it is not a tree.

Graphs will be given as an array with each item being an array of integers which are the nodes that node is connected to.

For example, this graph:
```
0--1
|  |
2--3--4
```
has array:
```
[[1,2], [0,3], [0,3], [1,2,4], [3]]
```
Note that it is also not a tree, because it contains closed path:
```
0->1->3->2->0
```
A node with no connections is an empty array
Note that if node 0 is connected to node 1, node 1 is also connected to node 0. This will always be true.
The order in which each connection is listed for each node also does not matter.

Good luck!

```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 = "def isTree(matrix):\n    '''depth first search; tree on n vertices has exactly n-1 edges'''\n    vertices = set(range(len(matrix)))\n    stack = [vertices.pop()]\n    while stack:\n        children = {y for y in matrix[stack.pop()] if y in vertices}\n        vertices.difference_update(children)\n        stack.extend(children)\n    return not vertices and sum(map(len,matrix)) == 2 * len(matrix) - 2"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'isTree'
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: 6024