# Task
 A lock has `n` buttons in it, numbered from `1 to n`. To open the lock, you have to press all buttons in some order, i.e. a key to the lock is a permutation of the first `n` integers. If you push the right button in the right order, it will be pressed into the lock. Otherwise all pressed buttons will pop out. When all buttons are pressed into the lock, it opens.
 
 Your task is to calculate the number of times you've got to push buttons in order to open the lock in the `worst-case scenario`.

# Example

 For `n = 3`, the result should be `7`.
 ```
 Let's assume the right order is 3-2-1.
 In the worst-case scenario, we press the buttons:
 Press 1, wrong, button 1 pop out
 Press 2, wrong, button 2 pop out
 Press 3, right, button 3 pressed in
 Press 1, wrong, button 1,3 pop out
 Press 3, right, button 3 pressed in
 Press 2, right, button 2 pressed in
 Press 1, right, button 1 pressed in
 We pressed button total 7 times.``` 
 
 For `n = 4`, the result should be `14`.
 ```
 Let's assume the right order is 4-3-2-1.
 In the worst-case scenario, we press the buttons:
 Press 1, wrong, button 1 pop out
 Press 2, wrong, button 2 pop out
 Press 3, wrong, button 3 pop out
 Press 4, right, button 4 pressed in
 Press 1, wrong, button 1,4 pop out
 Press 4, right, button 4 pressed in
 Press 2, wrong, button 2,4 pop out
 Press 4, right, button 4 pressed in
 Press 3, right, button 3 pressed in
 Press 1, wrong, button 1,3,4 pop out
 Press 4, right, button 4 pressed in
 Press 3, right, button 3 pressed in
 Press 2, right, button 2 pressed in
 Press 1, right, button 1 pressed in
 We pressed button total 14 times.``` 

# Input/Output


 - `[input]` integer `n`

  The number of buttons in the lock.
  
  `0 < n ≤ 2000`


 - `[output]` an integer

 The number of times you've got to push buttons in the `worst-case scenario`.

```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 press_button(n):\n  return sum((n-i)*(i+1)-i for i in range(n))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'press_button'
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: 5412