The palindromic number `595` is interesting because it can be written as the sum of consecutive squares: `6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2 + 12^2 = 595`.

There are exactly eleven palindromes below one-thousand that can be written as consecutive square sums. Note that `1 = 0^2 + 1^2` has not been included as this problem is concerned with the squares of positive integers.

Given an input `n`, find the count of all the numbers less than `n` that are both palindromic and can be written as the sum of consecutive squares.

For instance: `values(1000) = 11`. See test examples for more cases.  

Good luck!

This Kata is borrowed from [Project Euler #125](https://projecteuler.net/problem=125)

If you like this Kata, please try:

[Fixed length palindromes](https://www.codewars.com/kata/59f0ee47a5e12962cb0000bf)

[Divisor harmony](https://www.codewars.com/kata/59bf97cd4f98a8b1cd00007e)

```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 = 'sumSquaresToN = lambda n: n*(n+1)*(2*n+1)//6\n\nmemo = set()\n\ndef values(n):\n    lastMax = max(memo) if memo else 0\n    if lastMax >= n:\n        return sum( x < n for x in memo )\n    \n    top = int( (1 + (1+2*(n-1))**.5) // 2 )           # Value of the top number for a sum of two consecutive squares under n: (top-1)**2 + top**2 <= n    \n    for a in range(top, 1, -1):\n        va = sumSquaresToN(a)                         # sum of squares of 1, 2, 3, ..., a\n        if va <= lastMax: break                       # va is greater than all the values generated with the inner loop, so if too small to generate new values, exit\n\n        for b in range(a-2, -1, -1):\n            v = va - sumSquaresToN(b)                 # current value\n            if v >= n: break                          # going down with the values of b, v increase at each execution. Allow to exit the loop when generated values become to big (and useless for the current call)\n            if v == int(str(v)[::-1]): memo.add(v)\n            \n    return len(memo)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'values'
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: 5912