This year $p$ footballers and $q$ cricketers have been invited to participate in IPL (Indian Programming League) as guests. You have to accommodate them in $r$ rooms such that-
- No room may remain empty.
- A room may contain either only footballers or only cricketers, not both.
- No cricketers are allowed to stay alone in a room.
Find the number of ways to place the players. Note though, that all the rooms are identical. But each of the cricketers and footballers are unique. 
Since the number of ways can be very large, print the answer modulo $998,244,353$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains three space-separated integers $p$, $q$ and $r$ denoting the number of footballers, cricketers and rooms.

-----Output-----
For each test case, output the number of ways to place the players modulo $998,244,353$.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le p, q, r \le 100$

-----Example Input-----
4
2 1 4
2 4 4
2 5 4
2 8 4

-----Example Output-----
0
3
10
609

-----Explanation-----
Example case 2: Three possible ways are:
- {Footballer 1}, {Footballer 2}, {Cricketer 1, Cricketer 2}, {Cricketer 3, Cricketer 4}
- {Footballer 1}, {Footballer 2}, {Cricketer 1, Cricketer 3}, {Cricketer 2, Cricketer 4}
- {Footballer 1}, {Footballer 2}, {Cricketer 1, Cricketer 4}, {Cricketer 2, Cricketer 3}    
Please note that the rooms are identical.

```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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '#copy from all submission only for learn \nMOD = 998244353\n\nfball = [ [0]*101 for _ in range(101) ]\n\ncric = [ [0]*101 for _ in range(101) ] \n\n\n\ndef calSNum(n, r):\n if n == r or r == 1:\n  fball[r][n] = 1\n  return\n if n > 0 and r > 0 and n > r:\n  fball[r][n] = (fball[r-1][n-1]%MOD + (r*fball[r][n-1])%MOD )%MOD\n  return\n fball[r][n] = 0\n  \n\ndef calASNum(n, r):\n if n == 0 and r == 0 :\n  cric[r][n] = 0\n  return\n if n >= 2 and r == 1:\n  cric[r][n] = 1\n  return \n if r > 0 and n > 0 and n >= 2*r:\n  cric[r][n] = ((r*cric[r][n-1])%MOD + ((n-1)*cric[r-1][n-2])%MOD )%MOD\n  return\n cric[r][n] = 0\n \n\ndef preCompute():\n for r in range(1,101):\n  for n in range(1, 101):\n   calSNum(n, r)\n   calASNum(n, r)\n\n \ndef main():\n \n preCompute()\n for _ in range(int(input())):\n\n  f, c, r = list(map(int, input().split()))\n\n  ans = 0\n  \n  if f + (c//2) >= r:\n   minv = min(f, r)\n   \n   for i in range(1, minv+1):\n    if r-i <= c//2:\n     ans = (ans + (fball[i][f] * cric[r-i][c])%MOD )%MOD\n   \n  print(ans)\n   \ndef __starting_point():\n main()\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 422763