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        '''\n        # Notes:\n            example n = 3\n                                P1         P2     P3 \n                             P2    P3   D1\n                        P3   D1  D2\n                     D1  D2 D3\n                  D2  D3\n        # Approach:\n            Dynamic Programming\n            opt[i][j]   i represents how many delivery are holding\n                        j represents how many remaining delivery\n                        output = opt[0][n]\n                       \n                                OPT[0][3]\n                                3*OPT[1][2]\n                        1*OPT[0][2]        2*OPT[2][1]\n                        2*OPT[1][1]     2*OPT[1][1]  1*OPT[3][0]\n                    1*OPT[0][1] 1*OPT[2][0]\n                    \n            OPT[i][j] = i*opt[i-1][j] + j*opt[i+1][j-1]\n                                \n        '''\n        opt = [[0 for _ in range(n+1)] for _ in range(n+1)]\n\n        for j in range(n+1):\n            for i in range(n+1):\n                if j == n:\n                    opt[i][j] = j*opt[i+1][j-1]\n                    return opt[0][n] % (pow(10, 9)+7)\n                if i == 0 and j == 0:\n                    continue\n                if i == 0 and j == 1:\n                    opt[i][j] = 1\n                    continue\n                if i == 1 and j == 0:\n                    opt[i][j] = 1\n                    continue\n                if i == 0:\n                    opt[i][j] = j*opt[i+1][j-1]\n                elif j == 0:\n                    opt[i][j] = i*opt[i-1][j]\n                else:\n                    if i + j > n:\n                        break\n                    opt[i][j] = i*opt[i-1][j] + j*opt[i+1][j-1]\n                    \n        \n        #return opt[0][n] % (pow(10, 9)+7)\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: 6558