Given a positive integer N, how many ways can we write it as a sum of consecutive positive integers?
Example 1:
Input: 5
Output: 2
Explanation: 5 = 5 = 2 + 3
Example 2:
Input: 9
Output: 3
Explanation: 9 = 9 = 4 + 5 = 2 + 3 + 4
Example 3:
Input: 15
Output: 4
Explanation: 15 = 15 = 8 + 7 = 4 + 5 + 6 = 1 + 2 + 3 + 4 + 5
Note: 1 <= N <= 10 ^ 9.

```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 consecutiveNumbersSum(self, N: int) -> int:\n        self.primes=[2,3,5,7,11]\n        self.get_primes(N)\n        # print(self.primes)\n        self.get_factors(2*N)\n        # print(self.factor_arr)\n        ans=0\n        for factor in self.factor_arr:\n            x=((2*N)/factor-factor-1)/2\n            # print(x)\n            if x<0:\n                continue#break\n            if x%1==0:\n                # print(x)\n                ans+=1\n        return ans\n            \n            \n        \n    \n    def get_factors(self,n):\n        self.factors={1: 1}\n        self.factor_arr=[1]\n        i=0\n        while(n>1 and i<len(self.primes)):\n            prime=self.primes[i]\n            pw=0\n            # print(n,prime)\n            while(n%prime==0):\n                n=n/prime\n                pw+=1\n            while(pw):\n                    length=len(self.factor_arr)\n                    for fi in range(length):\n                        nf=self.factor_arr[fi]*prime\n                        if nf not in self.factors:\n                            self.factors[nf]=1\n                            self.factor_arr+=[nf]\n                    pw-=1\n            # print(\\"p-f_arr\\",prime,self.factor_arr)\n            i+=1\n        if n>1:\n                length=len(self.factor_arr)\n                for i in range(length):\n                    nf=self.factor_arr[i]*n\n                    if nf not in self.factors:\n                        self.factors[nf]=1\n                        self.factor_arr+=[nf]\n        return\n                        \n                \n    def get_primes(self,n):\n        last_prime=self.primes[-1]\n        k=last_prime//6\n        adds=[1,5]\n        i=adds.index(last_prime%6)\n        i+=1\n        if i==2:\n                k+=1\n                i=0\n        num=6*k+adds[i]\n        \n        while(num*num<n):\n            if self.is_prime(num):\n                self.primes+=[num]\n            i=i+1\n            if i==2:\n                k+=1\n                i=0\n            num=6*k+adds[i]\n    \n    def is_prime(self,n):\n        for prime in self.primes:\n            if prime*prime>n:\n                break\n            if n%prime==0:\n                return False\n        return True'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'consecutiveNumbersSum'
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: 6986