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 = 'def func(n,m,z,l,r,b):\n l=l+r\n if(l>=n*(m-1)):\n  return min(n*m,l+z+b)\n x=l/(m-1)\n ans=x*(m-1)\n x=min(b,x)\n ans=ans+x\n b=b-x\n x=l%(m-1)\n ans=ans+x\n x=m-x\n x=min((x/2)+(x%2),b)\n ans=ans+x\n b=b-x\n x=n-(l/(m-1))\n x=x-1\n x=min(b,x*((m/2)+(m%2)))\n ans=ans+x\n z=min(z,n*m-ans)\n ans=ans+z\n return ans\ndef func2(n,m,z,l,r,b):\n l=l+r\n if(l>=n*(m-1)):\n  return min(n*m,l+z+b)\n x=l/(m-1)\n ans=x*(m-1)\n n2=n-x\n x=min(b,x)\n ans=ans+x\n b=b-x\n l=l%(m-1)\n x=l/n2\n ans=ans+x*n2\n m=m-x\n l=l%n2\n ans1=ans+func(n2,m,z,l,0,b)\n ans2=0\n ans3=0\n if(l>0):\n  ans2=ans+l\n  x=min(z,n2-l)\n  ans2=ans2+x\n  z=z-x\n  m=m-1\n  ans2=ans2+func(n2,m,z,0,0,b)\n  z=z+x\n  m=m+1\n  ans3=ans+l\n  x=min(b,n2-l)\n  ans3=ans3+x\n  b=b-x\n  m=m-2\n  ans3=ans3+func(n2,m,z,0,0,b)\n return max(ans1,ans2,ans3)\nt=eval(input())\nfor _ in range(0,t):\n n,m,z,l,r,b=list(map(int,input().split()))\n a=func(n,m,z,l,r,b)\n a=max(a,func2(n,m,z,l,r,b))\n print(a) '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17019