# Task

You are given a positive integer `n`. We intend to make some ascending sequences according to the following rules:

 1. Make a sequence of length 1: [ n ]

 2. Or, insert a number to the left side of the sequence. But this number can not exceed half of the first number of the sequence. 

 3. Follow rule 2, continue insert number to the left side of the sequence.

Your task is to count the number of all possible sequences, and return it.

If you do not understand the task, please read the rewritten version below:

You are given a positive integer `n`. Your task is to count the number of such sequences: 

- It should be an ascending sequence;

- It should end with number `n`.

- Each number in the sequence should smaller or equals to the half of its right, except for the last number `n`.

- We define that a sequence containing only a number `n` is a valid ascending sequence.

# Examples

For `n = 6`, the output should be `6`.

All sequences we made are:

```
[6]

insert a number to the left:

[1,6]
[2,6]
[3,6]

continue insert number:

[1,2,6]
[1,3,6]
```
There are 6 sequences in total.


For `n = 10`, the output should be `14`.

All sequences we made are:

```
[10]

insert a number to the left:

[1,10]
[2,10]
[3,10]
[4,10]
[5,10]

continue insert number:

[1,2,10]
[1,3,10]
[1,4,10]
[2,4,10]
[1,5,10]
[2,5,10]

continue insert number:

[1,2,4,10]
[1,2,5,10]

```
There are 14 sequences in total.

# Note

- `1 <= n <= 1000`

- `3` fixed testcases

- `100` random testcases, testing for correctness of solution

- All inputs are valid.

- If my reference solution gives the wrong result in the random tests, please let me know(post an issue).

```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 make_sequences(n):\n    a = [1]\n    for i in range(1, n + 1):\n        a.append(a[i - 1] if i % 2 else a[i // 2] + a[i - 1])\n    return a.pop()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'make_sequences'
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: 5468