In number theory, Euler's totient is an arithmetic function, introduced in 1763 by Euler, that counts the positive integers less than or equal to `n` that are relatively prime to `n`. Thus, if `n` is a positive integer, then `φ(n)`, notation introduced by Gauss in 1801, is the number of positive integers `k ≤ n` for which `gcd(n, k) = 1`.  
The totient function is important in number theory, mainly because it gives the order of the multiplicative group of integers modulo `n`. The totient function also plays a key role in the definition of the RSA encryption system.

For example `let n = 9`.  
Then `gcd(9, 3) = gcd(9, 6) = 3` and `gcd(9, 9) = 9`.  
The other six numbers in the range `1 ≤ k ≤ 9` i.e. `1, 2, 4, 5, 7, 8` are relatively prime to `9`.  
Therefore, `φ(9) = 6`.  
As another example, `φ(1) = 1` since `gcd(1, 1) = 1`.

There are generally two approaches to this function:

* Iteratively counting the numbers `k ≤ n` such that `gcd(n,k) = 1`.

* Using the Euler product formula.  
  This is an explicit formula for calculating `φ(n)` depending on the prime divisor of `n`:  
  `φ(n) = n * Product (1 - 1/p)` where the product is taken over the primes `p ≤ n` that divide `n`.  
  For example: `φ(36) = 36 * (1 - 1/2) * (1 - 1/3) = 36 * 1/2 * 2/3 = 12`.  
  This second method seems more complex and not likely to be faster, but in practice we will often look for `φ(n)` with `n` prime. It correctly gives `φ(n) = n - 1` if `n` is prime. 

You have to code the Euler totient function, that takes an integer `1 ≤ n` as input and returns `φ(n)`.

```if:javascript
You do have to check if `n` is a number, is an integer and that `1 ≤ n`; if that is not the case, the function should return `0`.
```

```if:python
You do have to check if `n` is a number, is an integer and that `1 ≤ n`; if that is not the case, the function should return `0`.
```

```if:racket
`n` is always a positive integer.
```

Input range: `1 ≤ n ≤ 1e10`

```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 = '\ndef totient(n):\n    if not isinstance(n, int) or n<1:\n        return 0\n    factor=prime_factorization(n)\n    up=1\n    down=1\n    for i in factor:\n        up*=(i-1)\n        down*=i\n    return n*up//down\ndef prime_factorization(n):\n    res=set()\n    while n>1 and n%2==0:\n        res.add(2)\n        n//=2\n    while n>1 and n%3==0:\n        res.add(3)\n        n//=3\n    factor=5\n    while factor*factor<=n:\n        if n%factor==0:\n            res.add(factor)\n            n//=factor\n            factor=5\n        else:\n            factor+=1\n    if n>1:\n        res.add(n)\n    return res'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'totient'
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: 5848