##Background - the Collatz Conjecture:

Imagine you are given a positive integer, `n`, then:

* if `n` is even, calculate: `n / 2`
* if `n` is odd, calculate: `3 * n + 1`

Repeat until your answer is `1`. The Collatz conjecture states that performing this operation repeatedly, you will always eventually reach `1`.

You can try creating Collatz sequences with [this](http://www.codewars.com/kata/5286b2e162056fd0cb000c20) kata. For further information, see the [wiki page](https://en.wikipedia.org/wiki/Collatz_conjecture).

##Now! Your task:

**Given an array of positive integers, return the integer whose Collatz sequence is the longest.**

Example:

```python
longest_collatz([2, 4, 3])==3
```

Explanation: The Collatz sequence for `2` has a length of `1`, the sequence for `4` has a length of `2`, and the sequence for `3` has a length of `7`. So from our array, the integer `3` is the one with the longest Collatz sequence.

Hence, your function should return `3`.

##Note:

There may be more than one answer, i.e. two or more integers produce the longest Collatz sequence, because they happen to have sequences of the same length. **In this case, your function should return the integer that appears first in the array.**

Example:
Given an array: `[2, 5, 32]`, both `5` and `32` have Collatz sequences of length 5. These are also the longest sequences from our array.

In this case, our function returns `5`, because `5` comes before `32` in our array.

```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 functools import lru_cache\n\n@lru_cache(maxsize=None)\ndef collatz(n):\n    return n != 1 and 1 + collatz(3*n+1 if n&1 else n>>1)\n\ndef longest_collatz(input_array):\n    return max(input_array, key=collatz)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'longest_collatz'
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: 31972