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 = 'from sys import *\ndef eq_solve(v0, v1, u0, u1):\n    den = u0 - v0\n    num = u1 - v1\n    if den != 0:\n        return num / den\n    return 1\n \ndef solve(p, q, r, a, b, c, rs):\n    if p == a and q == b and r == c:\n        return rs\n    if rs >= 2:\n        return 3\n    res = 3\n    adds = [a - p, b - q, c - r]\n    muls = []\n    if p != 0:\n        muls.append(a / p)\n    if q != 0:\n        muls.append(b / q)\n    if r != 0:\n        muls.append(c / r)\n    muls.append(eq_solve(p, a, q, b))\n    muls.append(eq_solve(p, a, r, c))\n    muls.append(eq_solve(q, b, r, c))\n    msks = 2 ** 3\n    for msk in range(msks):\n        for add in adds:\n            np = p\n            nq = q\n            nr = r\n            if (msk & 1) > 0:\n                np += add\n            if (msk & 2) > 0:\n                nq += add\n            if (msk & 4) > 0:\n                nr += add\n            res = min(res, solve(np, nq, nr, a, b, c, rs + 1))\n        for mul in muls:\n            np = p\n            nq = q\n            nr = r\n            if (msk & 1) > 0:\n                np *= mul\n            if (msk & 2) > 0:\n                nq *= mul\n            if (msk & 4) > 0:\n                nr *= mul\n            res = min(res, solve(np, nq, nr, a, b, c, rs + 1))\n    return res\n        \nt = int(stdin.readline())\nwhile t > 0:\n    p,q,r = map(int,stdin.readline().split())\n    a,b,c = map(int,stdin.readline().split())\n    print(solve(p,q,r,a,b,c,0))\n    t -= 1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 20083