Probably everyone has experienced an awkward situation due to shared armrests between seats in cinemas. A highly accomplished cinema manager named "Chef" decided to solve this problem.

When a customer wants to buy a ticket, the clerk at the ticket window asks the visitor if they need the armrests, and if so, which of them: left, right, or both. We know that out of the audience expected to show up, L of them only need the left armrest, R of them need just the right one, Z need none and B need both. Your task is to calculate the maximum number of people that can attend the show. In the cinema hall there are N rows with M seats each. There is only one armrest between two adjacent seats. Seats at the beginning and at the end of the row have two armrests

-----Input-----

Input begins with an integer T: the number of test cases.

Each test case consists of a single line with 6 space-separated integers: N, M, Z, L, R, B.

-----Output-----

For each test case, output a line containing the answer for the task.

-----Constraints and Subtasks-----
- 1 ≤ T ≤ 105 
Subtask 1 : 10 points 
- 1 ≤ N, M ≤ 3 
- 0 ≤ Z, L, R, B ≤ 3 
Subtask 2 : 20 points 
- 1 ≤ N, M ≤ 30 
- 0 ≤ Z, L, R ≤ 30 
- 0 ≤ B ≤ 109 
Subtask 3 : 30 points
- 1 ≤ N, M ≤ 106 
- 0 ≤ Z, L, R ≤ 106 
- 0 ≤ B ≤ 1016 
Subtask 4 : 40 points
- 1 ≤ N, M ≤ 108 
- 0 ≤ Z, L, R, B ≤ 1016 

-----Example-----
Input:2
2 2 3 2 1 1
3 3 1 2 0 9

Output:4
8

-----Explanation-----
'L' - needs left

'R - needs right

'Z' - doesn't need any

'B' - needs both

'-' - empty place

Example case 1.
ZZ

ZB
Example case 2.
LLB

BZB

B-B

```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 = 't=int(input())\nwhile(t):\n t-=1\n n,m,z,l,r,b=list(map(int,input().split()))\n if(m!=1):\n  if(b>=n):\n   ba=n\n   bl=b-n\n  else:\n   ba=b\n   b1=0\n  if(ba==n):\n   if((l+r)>=n*(m-1)):\n    ans=n*m\n   else:\n    w=(l+r)%(m-1)\n    la=l\n    ll=0\n    ra=r\n    rl=0\n    x=(m-1)/2\n    y=n-(l+r)/(m-1)\n    if(w==0):\n     if(bl>=(x*y)):\n      ba+=x*y\n      bl=b-ba\n     else:\n      ba=b\n      bl=0\n    else:\n     y-=1\n     u=m-1-w\n     if(bl>=(u/2+x*y)):\n      ba+=(u/2+x*y)\n      bl=b-ba\n     else:\n      ba=b\n      bl=0\n    za=min(n*m-la-ra-ba,z)\n    zl=z-za\n    ans=min(n*m,la+ra+ba+za)\n  else:\n   if((l+r)>=n*m-b):\n    ans=n*m\n   else:\n    la=l\n    ll=0\n    ra=r\n    rl=0\n    za=min(n*m-la-ra-ba,z)\n    zl=z-za\n    ans=min(n*m,la+ra+ba+za)\n else:\n  ans=min(n*m,l+r+z+b)\n print(ans)\n      \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13607