Given n orders, each order consist in pickup and delivery services. 
Count all valid pickup/delivery possible sequences such that delivery(i) is always after of pickup(i). 
Since the answer may be too large, return it modulo 10^9 + 7.
 
Example 1:
Input: n = 1
Output: 1
Explanation: Unique order (P1, D1), Delivery 1 always is after of Pickup 1.

Example 2:
Input: n = 2
Output: 6
Explanation: All possible orders: 
(P1,P2,D1,D2), (P1,P2,D2,D1), (P1,D1,P2,D2), (P2,P1,D1,D2), (P2,P1,D2,D1) and (P2,D2,P1,D1).
This is an invalid order (P1,D2,P2,D1) because Pickup 2 is after of Delivery 2.

Example 3:
Input: n = 3
Output: 90

 
Constraints:

1 <= n <= 500

```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 countOrders(self, n: int) -> int:\n        # 9:41\n        # we just want to make sure delivery i happens before pick up i\n        # we can save lot of recursive calls by using maths\n        \n#         n*[(n-1),1]\n#                    n-2\n                    \n#         p,d\n#         n,0\n        \n#         p=n\n#         d=0\n        \n#         p=n-1\n#         d=1\n        \n#         p=n-2   or p=n-1\n#                d=0\n#         d=2.\n        \n        # @lru_cache(None)\n        # def factorial(x):\n        #     fact=1\n        #     for i in range(1,x+1):\n        #         fact*=i\n        #     return fact\n        mod=10**9+7\n        facts=[1]\n        for i in range(1,n+1):\n            facts.append(facts[-1]*i)\n        \n        \n        @lru_cache(None)\n        def ways(pickOptions,deliverOptions):\n            nonlocal mod\n            ans=0\n            if pickOptions>0 and deliverOptions>0:\n                ans+=ways(pickOptions-1,deliverOptions+1)*pickOptions\n                ans+=ways(pickOptions,deliverOptions-1)*deliverOptions\n            elif pickOptions>0 and deliverOptions==0:\n                ans+=ways(pickOptions-1,deliverOptions+1)*pickOptions\n            elif deliverOptions>0 and pickOptions==0:\n                ans+=facts[deliverOptions]\n            return ans%mod\n        return ways(n,0)\n    \n        # dp=[]\n        # for p in range(n+1):\n        #     for d in range()\n        \n                \n                \n                \n            \n        \n        \n        \n            \n        \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'countOrders'
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: 8206