Consider the following operations on a triple of integers. In one operation, you should:
- Choose an integer $d$ and an arithmetic operation ― either addition or multiplication.
- Choose a subset of elements of the triple.
- Apply the arithmetic operation to each of the chosen elements, i.e. either add $d$ to each of them or multiply each of them by $d$.
For example, if we have a triple $(3, 5, 7)$, we may choose to add $3$ to the first and third element, and we get $(6, 5, 10)$ using one operation.
You are given an initial triple $(p, q, r)$ and a target triple $(a, b, c)$. Find the minimum number of operations needed to transform $(p, q, r)$ into $(a, b, c)$.

-----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 line of each test case contains three space-separated integers $p$, $q$ and $r$.
- The second line contains three space-separated integers $a$, $b$ and $c$.

-----Output-----
For each test case, print a single line containing one integer ― the minimum required number of operations.

-----Constraints-----
- $1 \le T \le 1,000$
- $|p|, |q|, |r|, |a|, |b|, |c| \le 10^9$

-----Subtasks-----
Subtask #1 (10 points): $|p|, |q|, |r|, |a|, |b|, |c| \le 10$
Subtask #2 (90 points): original constraints

-----Example Input-----
2
3 5 7
6 5 10
8 6 3
9 7 8

-----Example Output-----
1
2

-----Explanation-----
Example case 1: We add $3$ to the first and third element of $(3, 5, 7)$ to form $(6, 5, 10)$.
Example case 2: We can add $1$ to each element to form $(9, 7, 4)$ and then multiply the third element by $2$.

```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 = "import sys\r\ndef fop(s,end='\\n'): sys.stdout.write(str(s)+end)\r\ndef fip(): return sys.stdin.readline().strip()\r\nfintinp = lambda : int(fip()) \r\ndef flistinp(func= int): return list(map(func,fip().split())) \r\ndef fnsepline(n,func=str): return [func(fip()) for _ in range(n)]\r\nfrom functools import lru_cache\r\n#-------------------code------------------------\r\n@lru_cache(maxsize=1<<10)\r\ndef byeqs(pqr, abc):\r\n    # f_ans = 3\r\n    p,q,r = pqr\r\n    a,b,c = abc\r\n    # zeq = a*(r-q) + b*(p-r) + c*(q-p)\r\n    # m=n=None # for y = mx + n\r\n    muls = [] \r\n    # if zeq==0:\r\n    try:\r\n        if p!=q:\r\n            m_ = (a-b)//(p-q)\r\n            muls.append(m_)\r\n    except: pass\r\n    try:\r\n        if p!=r:\r\n            m_ = (a-c)//(p-r)\r\n            muls.append(m_)\r\n    except: pass\r\n    try:\r\n        if q!=r:\r\n            m_ = (b-c)//(q-r)\r\n            muls.append(m_)\r\n    except: pass\r\n    return muls\r\n\r\n@lru_cache(maxsize=1<<10)\r\ndef recSolver(pqr, abc, ans = 0):\r\n    if pqr == abc: return ans \r\n    if ans>=2: return 3\r\n    adds = [abc[i]-pqr[i] for i in range(3)]\r\n    muls = [abc[i]//pqr[i] if pqr[i]!=0 else 0 for i in range(3)] + byeqs(pqr, abc)\r\n    f_ans = 3 \r\n    for ss in range(8):\r\n        for a in adds:\r\n            pqr_copy = list(pqr)\r\n            for i in [1,2,4]:\r\n                if ss&i:\r\n                    pqr_copy[i>>1]+=a \r\n            f_ans = min(f_ans, recSolver(tuple(pqr_copy), tuple(abc), ans+1))\r\n            \r\n        for m in muls:\r\n            pqr_copy = list(pqr)\r\n            for i in [1,2,4]:\r\n                if ss&i:\r\n                    pqr_copy[i>>1]*=m \r\n            f_ans = min(f_ans, recSolver(tuple(pqr_copy), tuple(abc), ans+1))\r\n    return f_ans\r\n                \r\nfor _ in range(fintinp()):\r\n    pqr = flistinp()\r\n    abc = flistinp()\r\n    fop(recSolver(tuple(pqr), tuple(abc), 0))"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 265342