Initially on a notepad only one character 'A' is present. You can perform two operations on this notepad for each step: 

Copy All: You can copy all the characters present on the notepad (partial copy is not allowed).
Paste: You can paste the characters which are copied last time.




Given a number n. You have to get exactly n 'A' on the notepad by performing the minimum number of steps permitted. Output the minimum number of steps to get n 'A'. 


Example 1:

Input: 3
Output: 3
Explanation:
Intitally, we have one character 'A'.
In step 1, we use Copy All operation.
In step 2, we use Paste operation to get 'AA'.
In step 3, we use Paste operation to get 'AAA'.




Note:

The n will be in the range [1, 1000].

```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 minSteps(self, n):\n         """\n         :type n: int\n         :rtype: int\n         """\n         \n         if n == 1:\n             return 0\n         \n         # just manually does the first factor\n         # useless step\n         \n         #lf = min(self.primes(n))\n         \n         #steps = lf\n         #divs = n // lf\n         \n         \n         return self.calcsteps(0, n) \n         # return self.calcsteps(steps, lf)   \n         \n         \'\'\'\n         # this cleaner version of my approach starts at the lowest factor, then moves up when the number can no longer be cleanly divided\n         # d stands for divisor (?)\n         # both solutions run at 40ms\n         \n         ans = 0\n         d = 2\n         while n > 1:\n             while n % d == 0:\n                 ans += d\n                 n /= d\n             d += 1\n         return ans\n         \'\'\'\n     def isprime(self, n):\n         if n == 2 or n == 3:\n             return True\n         if n % 2 == 0 or n % 3 == 0:\n             return False\n \n         i = 5\n         w = 2\n \n         while i * i <= n:\n             if n % i == 0:\n                 return False\n \n             i += w\n             w = 6 - w\n \n         return True\n     \n     def primes(self, n):\n         # gets all prime factors of n\n         primfac = []\n         d = 2\n         while d*d <= n:\n             while (n % d) == 0:\n                 primfac.append(d)\n                 n //= d\n             d += 1\n         if n > 1:\n             primfac.append(n)\n         return primfac\n     \n     def calcsteps(self, steps, divs):\n         if self.isprime(divs):\n                 return divs + steps\n         \n         primes = self.primes(divs)\n         # if a factor is three, you have to copy n, then paste it twice. 1 + 2 = 3, 1 + n - 1 = n\n         # therefore, the number of steps is the sum of the primes\n         \n         return steps + sum(primes)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minSteps'
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: 5614