In the morning all the doors in the school are closed. The school is quite big: there are **N** doors. Then pupils start coming. It might be hard to believe, but all of them want to study! Also, there are exactly **N** children studying in this school, and they come one by one.

When these strange children pass by some doors they change their status (i.e. Open -> Closed, Closed -> Open). Each student has their number, and each i-th student alters the status of every i-th door. For example: when the first child comes to the schools, he changes every first door (he opens all of them). The second one changes the status of every second door (he closes some doors: the 2nd, the 4th and so on). Finally, when the last one – the n-th – comes to the school, he changes the status of each n-th door (there's only one such door, though).

You need to count how many doors are left opened after all the students have come.

Example:

![](http://i.imgur.com/IqlOi2q.png)

*Here you can see red squares – closed doors, green – opened ones.*

Input:

> n – the number of doors and students, n ∈ N, n ∈ [1, 100000]

Output:

> o – the number of opened doors, o ∈ N

--- 

```
doors(5)
```

Should return

```
2
```

```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 = 'def doors(n):\n  allDoors = []\n  for i in range(0, n):\n    allDoors.append("closed")\n\n  for kid in range(1, n+1):\n    for door in range(kid-1, n, kid):\n        if allDoors[door] == "closed":\n          allDoors[door] = "open"\n        else:\n          allDoors[door] = "closed"\n\n  count = 0\n  for j in range(0, len(allDoors)):\n    if allDoors[j] == "open":\n      count+=1\n  return count'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'doors'
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: 5588