One of the first algorithm used for approximating the integer square root of a positive integer `n` is known as "Hero's method", 
named after the first-century Greek mathematician Hero of Alexandria who gave the first description
of the method. Hero's method can be obtained from Newton's method which came 16 centuries after. 

We approximate the square root of a number `n` by taking an initial guess `x`, an error `e` and repeatedly calculating a new approximate *integer* value `x` using: `(x + n / x) / 2`; we are finished when the previous `x` and the `new x` have an absolute difference less than `e`.

We supply to a function (int_rac) a number `n` (positive integer) and a parameter `guess` (positive integer) which will be our initial `x`. For this kata the parameter 'e' is set to `1`.

Hero's algorithm is not always going to come to an exactly correct result! For instance: if n = 25 we get 5 but for n = 26 we also get 5. Nevertheless `5` is the *integer* square root of `26`.

The kata is to return the count of the progression of integer approximations that the algorithm makes.

Reference:



Some examples:
```
int_rac(25,1): follows a progression of [1,13,7,5] so our function should return 4.

int_rac(125348,300): has a progression of [300,358,354] so our function should return 3.

int_rac(125348981764,356243): has a progression of [356243,354053,354046] so our function should return 3.
```

#

You can use Math.floor (or similar) for each integer approximation.
 
#

Note for JavaScript, Coffescript, Typescript:

Don't use the double bitwise NOT ~~ at each iteration if you want to have the same results as in the tests and the other languages.

```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 = 'int_rac=lambda n, x, c=1: int_rac(n, (x+n/x)/2 ,c+1) if abs(int(n**0.5)-x)>=1 else c'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'int_rac'
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: 5520