Mandarin chinese
, Russian and Vietnamese as well.
Let's denote $S(x)$ by the sum of prime numbers that divides $x$.
You are given an array $a_1, a_2, \ldots, a_n$ of $n$ numbers, find the number of pairs $i, j$ such that $i \neq j$, $a_i$ divides $a_j$ and $S(a_i)$ divides $S(a_j)$.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- First line of each testcase contains one integer $n$ — number of elements of the array.
- Second line of each testcase contains $n$ space-separated integers $a_1, a_2, \ldots, a_n$.

-----Output:-----
For each testcase, output in a single line number of pairs that each of it satisfies given conditions.

-----Constraints-----
- $1 \leq T \leq 100$
- $2 \leq n, a_i \leq 10^6$
- the sum of $n$ for all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #2 (20 points): $2 \leq n \leq 100$, $2 \leq a_i \leq 10^4$
Subtask #2 (80 points): original contsraints

-----Sample Input:-----
1
5
2 30 2 4 3

-----Sample Output:-----
6

-----EXPLANATION:-----
$S(2) = 2, S(30) = 2 + 3 + 5 = 10, S(4) = 2, S(3) = 3$. So using this information, the pairs of indicies are $(1,2)$, $(1, 3)$, $(1, 4)$, $(3, 1)$, $(3, 2)$, $(3, 4)$.

```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 bisect\nimport sys\nimport math\n\nt = int(input())\n\nM = 2000001\n\ns = [0 for x in range(M)]\n\nfor i in range(2,M):\n if (s[i] == 0):\n  s[i] = i;\n  for j in range(i*2,M,i):\n   s[j] += i\n\nwhile (t):\n\n n = int(input())\n a = [int(x) for x in input().split()]\n\n dict = {}\n m = 0\n for x in a:\n  m = max(x,m)\n  if (x in dict):\n   dict[x] += 1\n  else:\n   dict[x] = 1\n\n count = 0\n \n for k in dict.keys():\n  d = dict[k] * (dict[k] - 1)\n  count += d\n  for i in range(2,math.ceil(m/k)+1):\n   if (i*k in dict and s[i*k] % s[k] == 0):\n    d = dict[k] * dict[i*k] \n    count += d\n\n sys.stdout.write(str(count)+"\\n")\n \n \n t -= 1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 74575999