A sequence X_1, X_2, ..., X_n is fibonacci-like if:

n >= 3
X_i + X_{i+1} = X_{i+2} for all i + 2 <= n

Given a strictly increasing array A of positive integers forming a sequence, find the length of the longest fibonacci-like subsequence of A.  If one does not exist, return 0.
(Recall that a subsequence is derived from another sequence A by deleting any number of elements (including none) from A, without changing the order of the remaining elements.  For example, [3, 5, 8] is a subsequence of [3, 4, 5, 6, 7, 8].)
 


Example 1:
Input: [1,2,3,4,5,6,7,8]
Output: 5
Explanation:
The longest subsequence that is fibonacci-like: [1,2,3,5,8].

Example 2:
Input: [1,3,7,11,12,14,18]
Output: 3
Explanation:
The longest subsequence that is fibonacci-like:
[1,11,12], [3,11,14] or [7,11,18].

 
Note:

3 <= A.length <= 1000
1 <= A[0] < A[1] < ... < A[A.length - 1] <= 10^9
(The time limit has been reduced by 50% for submissions in Java, C, and C++.)

```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 = '\'\'\'\n----BRUTE (but is also smart)----\nKEY: use a set to hold all elements of input array.\nSo if you find a+b in the set, you can keep moving forward and updating 1 \\"jump\\" forward for a-->b, b--> a+b.\nThen continue. So change the if-check to a while loop.\n\nget every pair (i,j)\n    then try to find their next value in set. If found then update \n        holdj = j\n        j = i+j\n        i = holdj\n        len++\n    res = max(res,len)\nreturn res if res>2\n----big-O----\nO((N^2) * logM)\nN^2 to get each pair.\nlogM to get to the end of each fibonacci \\"chain\\"\n\n----dp----\ndp[a,b] = len of fib sequence ending with a,b\ndp[a,b] = dp[b-a,a]+1 , if val[b]-val[a] <val[a] and (val[b]-val[a]) exists in set\n        = 2            , if (val[b]-val[a],val[a]) doesnt exist in dp\nreturn the max of all dp cells, or [0]\n---big-O--\nO(N^2) for nested loop.\n\n        \n\'\'\'\nclass Solution:\n    def lenLongestFibSubseq(self, A: List[int]) -> int:\n        res = 0\n        if len(A)<=2:\n            return 0\n        find = set(A)\n        for i in range(len(A)-1):\n            for j in range(i+1,len(A)):\n                currLen = 2\n                a = A[i]\n                b = A[j]\n                while (a+b) in find: \n                    currLen+=1\n                    holdb = b   #you\'re not moving along i and j, but the actual values themselves. Because you already have the values you need in the set.\n                    b = a+b\n                    a = holdb\n                    res = max(currLen,res)\n        if res>2:\n            return res\n        else:\n            return 0\n                        \n                    \n                    \n                    \n                \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'lenLongestFibSubseq'
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: 5932