Consider the following series:

`1, 2, 4, 8, 16, 22, 26, 38, 62, 74, 102, 104, 108, 116, 122`

It is generated as follows:

* For single digit integers, add the number to itself to get the next element.
* For other integers, multiply all the non-zero digits and add the result to the original number to get the next element.

For example: `16 + (6 * 1) = 22` and `104 + (4 * 1) = 108`. 

Let's begin the same series with a seed value of `3` instead of `1`:

`3, 6, 12, 14, 18, 26, 38, 62, 74, 102, 104, 108, 116, 122`

Notice that the two sequences converge at `26` and are identical therefter. We will call the series seeded by a value of `1` the "base series" and the other series the "test series". 

You will be given a seed value for the test series and your task will be to return the number of integers that have to be generated in the test series before it converges to the base series. In the case above:
```Python
convergence(3) = 5, the length of [3, 6, 12, 14, 18]. 
```  

Good luck!

If you like this Kata, please try:

[Simple Prime Streaming](https://www.codewars.com/kata/5a908da30025e995880000e3)

[Unique digit sequence](https://www.codewars.com/kata/599688d0e2800dda4e0001b0)

[Divisor harmony](https://www.codewars.com/kata/59bf97cd4f98a8b1cd00007e)

```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 operator import mul\nfrom functools import reduce\n\n# generate base series\nbase, n = {1}, 1\nfor _ in range(2000):\n    n += reduce(mul, map(int, str(n).replace("0", "")))\n    base.add(n)\n\n\ndef convergence(n):\n    steps = 0\n    \n    while n not in base:\n        n += reduce(mul, map(int, str(n).replace("0", "")))\n        steps += 1\n    \n    return steps'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'convergence'
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: 5572