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 = 'class Solution:\n    def lenLongestFibSubseq(self, A: List[int]) -> int:\n        \n        # # straight forward N^2log(M)\n        # n = len(A)\n        # s = set()\n        # for i in A:\n        #     s.add(i)\n        # res = 0\n        # ll = 0\n        # for i in range(n):\n        #     for j in range(i+1,n):\n        #         f1 = A[i]\n        #         f2 = A[j]\n        #         if f1+f2 in s:\n        #             ll = 2\n        #         while f1+f2 in s:\n        #             ll += 1\n        #             tmp = f2\n        #             f2 = f1+f2\n        #             f1 = tmp\n        #         res = max(res,ll)\n        # return res\n        \n        # # DP N^2 time N^2 space using std. dp array, if using two key dict as dp \n        # n = len(A)\n        # d = {}\n        # for i in range(n):\n        #     d[A[i]] = i\n        # dp = [[0]*n for i in range(n)]\n        # res = 0\n        # for i in range(n):\n        #     for j in range(i+1,n):\n        #         tar = A[i]+A[j]\n        #         if tar in d:\n        #             k = d[tar]\n        #             dp[j][k] = max(dp[j][k], dp[i][j]+1, 3)\n        #             res = max(res,dp[j][k])\n        #     # print(res,i,j,dp)\n        # return res\n        \n        # DP using using two key dict as dp , N^2 time NlogM space\n        n = len(A)\n        d = {}\n        for i in range(n):\n            d[A[i]] = i\n        dp = {}\n        res = 0\n        for i in range(n):\n            for j in range(i+1,n):\n                tar = A[i]+A[j]\n                if tar in d:\n                    k = d[tar]\n                    dp[(j,k)] = max(dp.get((i,j),2)+1, dp.get((j,k),2))\n                    res = max(res,dp[(j,k)])\n            # print(res,i,j,dp)\n        return res\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: 7072