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 new_lenLongestFibSubseq(self, A: List[int]) -> int:\n        exists = set(A)                \n        max_length = 2\n        \n        for i in range(len(A)):\n            first = A[i]\n            for j in range(i):\n                second = A[j]\n                \n                start = second\n                curr_length = 2\n                \n                while (first + second) in exists:\n                    curr_length += 1\n                    curr = first + second\n                    second = first\n                    first = curr\n                max_length = max(max_length, curr_length)                    \n\n        if max_length < 3: return 0\n        return max_length\n        \n    \n    def lenLongestFibSubseq(self, A: List[int]) -> int:\n        exists = set(A)        \n        max_length = 2\n        \n        for i in range(len(A)):\n            for j in range(i):\n                b = A[i]                \n                a = A[j]\n                curr_length = 2\n                \n                while (a + b) in exists:\n                    curr_length += 1\n                    curr = a + b\n                    a = b\n                    b = curr\n                max_length = max(max_length, curr_length)\n        \n        if max_length <= 2: return 0\n        return max_length\n    \n    \n    \n    \n    \n    \n    \n    \n    \n    \n# [1,2,3,4,5,6,7,8]\n# \n# **** START == 1 **** \n#\n# second = 1\n# first = 2\n# curr_length = 3\n# curr = 3\n\n# cache[1] = max(cache[1]+1, 3)\n# cache[1] = max(0+1, 3)\n# cache[1] = 3\n# \n# second = 2\n# first = 3\n# curr_length = 4\n# curr = 5\n#\n# cache[1] = max(cache[1], curr_length)\n# cache[1] = max(3, 3)\n# cache[1] = 4\n#\n# second = 3\n# first = 5\n# curr_length = 5\n# curr = 8\n# \n# cache[1] = max(cache[1], 5)\n# cache[1] = 5\n#\n# second = 5\n# first = 8\n# curr_length = 6\n# curr = 13\n# \n# 13 not in A, next pair\n#\n#\n# **** START == 1 **** \n#\n# second = 1\n# first = 3\n# curr_length = 3\n# curr = 4\n# \n# cache[1] = max(5, 3)\n# cache[1] = 5\n#\n# second = 3\n# first = 4\n# curr = 7\n# curr_length = 4\n# \n# cache[1] = max(5, 4)\n# cache[1] = 5\n#\n# second = 4\n# first = 7\n# curr = 11\n# \n# 11 not in A, exit\n#\n\n \n                \n        \n        \n        \n        \n        \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: 5874