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        \n        \n#         https://leetcode.com/problems/longest-string-chain/discuss/585044/C%2B%2B-Using-unordered_map-and-DP\n# DP\n\n# 1. sort words in increasing order of length\n# 2. if len is same\n\n# LIS\n\n# dp[i] = longest word chain including index i\n# return max(dp)\n\n# dp[i] = max(dp[i], 1+ dp[j])\n# len(words[j]) + 1 = len(words[i])\n# ba, bda-> check all chars of j are in j in the same order\n\n# O(n^2*16)\n\n\n\n\n\nfrom collections import deque\n\ndef getKey(item):\n    return len(item)\n\ndef isPred(word1, word2):\n    word1 = list(word1)\n    word2 = list(word2)\n    q1 = deque(word1)\n    q2 = deque(word2)\n    while q1 and q2:\n        if q1[0] == q2[0]:\n            q1.popleft()\n            q2.popleft()\n        else:\n            q2.popleft()\n    if (not q1) and len(q2) <= 1:\n        return True\n    return False\n    \n\nclass Solution:\n    def longestStrChain(self, words: List[str]) -> int:\n        words.sort(key=getKey)\n        dp = [1]*len(words)\n        \n        for i in range(1, len(dp)):\n            for j in reversed(list(range(0, i))):\n                if len(words[j]) == len(words[i]):\n                    continue\n                elif len(words[j]) + 1== len(words[i]):\n                    if isPred(words[j], words[i]):\n                        dp[i] = max(dp[i], 1+ dp[j])\n                else:\n                    break\n        \n        return max(dp)\n        \n        \n\n\n# We can also think of thi problem as LIS problem \n\n\n# 1. Sort the words according to their length\n# Input: [\\"a\\",\\"b\\",\\"ba\\",\\"bca\\",\\"bda\\",\\"bdca\\"]\n# When you reach bdca ..check if dca is present..check if bca is present..check if bda is present..check if bdc is present\n# 2. So store each word in a hashmap form lookup in O(1)\n\n# 3. For each word in order of length, for each word2 which is word with one character removed, dp[word] = max(dp[word], dp[word2] + 1).\n# The maxm element in the dp array is the answer.\n\n\n\n# Clean implementation\n\n# https://leetcode.com/problems/longest-string-chain/discuss/376724/C%2B%2B-Simple-clean\n\n\n\n\n\n# Explaiantion:\n\n# https://leetcode.com/problems/longest-string-chain/discuss/295182/C%2B%2B-Bottom-Up-DP-solution-(with-Explanation)\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: 8778