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 = 'class Solution:\n    def longestStrChain(self, words: List[str]) -> int:\n        def isPredecessor(s1,s2):\n            add = False\n            s1_inx = 0\n            s2_inx = 0\n            while s1_inx < len(s1) and s2_inx < len(s2):\n                if s1[s1_inx] == s2[s2_inx]:\n                    s1_inx += 1\n                    s2_inx += 1\n                elif add == False:\n                    s2_inx += 1\n                    add = True\n                else:\n                    return False\n            return True\n        words = sorted(words, key = lambda x: len(x))\n        dp = [1] * len(words)\n        res = 1\n        for i in range(len(words)):\n            for j in range(0,i):\n                if len(words[i]) == len(words[j]):\n                    break\n                elif len(words[i]) - 1 > len(words[j]):\n                    continue\n                else:\n                    if isPredecessor(words[j],words[i]):\n                        dp[i] = max(dp[i],dp[j]+1)\n                        res = max(res,dp[i])\n        return res\n#         def isPre(word1,word2):\n#             flag=False\n#             indx1=0\n#             indx2=0\n#             while indx1 < len(word1) and indx2 < len(word2):\n#                 if word1[indx1] == word2[indx2]:\n#                     indx1 +=1\n#                     indx2+=1\n#                 elif flag == False:\n#                     indx2 +=1\n#                     flag =True\n#                 else:\n#                     return False\n#             return True\n        \n#         dp=len(words)*[1]\n#         words = sorted(words, key = lambda x: len(x))\n#         res=1\n#         for i in range(len(words)):\n#             for j in range(i):\n#                 if len(words[i])==len(words[j]):\n#                     break\n#                 elif len(words[i]) > len(words[j])+1:\n#                     continue\n#                 else:\n#                     if isPre(words[j],words[i]):\n#                         print(i)\n#                         dp[i]=max(dp[i],dp[j+1])\n#                         res=max(res,dp[i])\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: 6226