Given a list of words, each word consists of English lowercase letters.
Let's say word1 is a predecessor of word2 if and only if we can add exactly one letter anywhere in word1 to make it equal to word2.  For example, "abc" is a predecessor of "abac".
A word chain is a sequence of words [word_1, word_2, ..., word_k] with k >= 1, where word_1 is a predecessor of word_2, word_2 is a predecessor of word_3, and so on.
Return the longest possible length of a word chain with words chosen from the given list of words.
 
Example 1:
Input: ["a","b","ba","bca","bda","bdca"]
Output: 4
Explanation: one of the longest word chain is "a","ba","bda","bdca".

 
Note:

1 <= words.length <= 1000
1 <= words[i].length <= 16
words[i] only consists of English lowercase letters.

```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 collections import deque\n\nclass Solution:\n    def longestStrChain(self, words: List[str]) -> int:\n        \n        # return self.run_graph_solution(words)\n        return self.run_dp_solution(words)\n    \n    def run_dp_solution(self, words):\n        \n        mem = {'': 0}\n        \n        def inner(w):\n            if w in mem or w not in words:\n                return\n            \n            max_per_w = 1\n            for j in range(len(w)):\n                cur = w[:j] + w[j+1:]\n                if cur in mem:\n                    val = mem[cur] + 1\n                elif cur not in words:\n                    val = 1\n                else:\n                    inner(cur)\n                    val = mem[cur] + 1\n                if val > max_per_w:\n                    max_per_w = val\n            mem[w] = max_per_w\n            return\n        \n        for w in words:\n            inner(w)\n            \n        return max(mem.values())\n        \n    def run_graph_solution(self, words):\n        graph = {word: [] for word in words}\n        lengths = {k: [] for k in range(1, 17)}\n        into = {}\n        min_len = 17\n        max_len = 1\n        for word in words:\n            lengths[len(word)].append(word)\n            min_len = min(len(word), min_len)\n            max_len = max(len(word), max_len)\n                    \n        for k in range(min_len, max_len):\n            for word1 in lengths[k]:\n                for word2 in lengths[k + 1]:\n                    for i in range(len(word2)):\n                        if word2[:i] + word2[i+1:] == word1:\n                            graph[word1].append(word2)\n                            into[word2] = True     \n                            \n        sources = [word for word in words if word not in into]\n        max_len = 0\n        for s in sources:\n            max_len = max(max_len, self.run_bfs(s, graph))\n        return max_len\n                \n    def run_bfs(self, s, graph):\n        queue = deque(maxlen=len(list(graph.keys())))\n        queue.appendleft((s, 1))\n        summary = []\n        \n        while len(queue) > 0:\n            current_node, cur_len = queue.pop()\n            for word in graph[current_node]:\n                queue.appendleft((word, cur_len + 1))\n            summary.append(cur_len)\n        \n        return summary[-1]\n    \n    \n            \n            \n        \n        \n        \n        \n        \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'longestStrChain'
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: 6517