-----Problem Statement-----
Levy's conjecture, named after Hyman Levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime. To put it algebraically, 2n + 1 = p + 2q always has a solution in primes p and q (not necessary to be distinct) for n > 2. (Source: Wikipedia)
In this problem, given a positive integer N (not necessary to be odd integer greater than 5). Your task is to calculate how many distinct ordered pairs (p, q) such that N = p + 2q, where p and q are primes.

-----Input-----
The first line of input contains an integer T, denoting the number of test cases. Then T test cases follow.

Each test case consists of exactly one line containing an integer N.

-----Constraints-----
- 1 ≤ T ≤ 100000 (105)
- 1 ≤ N ≤ 10000 (104)

-----Output-----
For each test case, output the number of ordered pairs (p, q) of primes such that N = p + 2q.

-----Example-----
Input:
3
2
7
11

Output:
0
1
2

-----Explanation-----
Case #1: There are no ordered pairs (p, q) such that p + 2q = 2.
Case #2: There is only one ordered pair (p, q) = (3, 2) such that p + 2q = 7.
Case #3: There are two ordered pairs (p, q) = (7, 2), (5, 3) such that p + 2q = 11.

```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 sieve(n):\n '''\n    Sieve of eratosthenes\n    Returns primesd: dictionary of primes upto n\n      primesl: list of primes upto n\n    '''\n l = [True]*(n+1)\n l[0] = False\n l[1] = False\n for i in range(2, n+1):\n  j = i*i\n  while j < n+1:\n   l[j]=False\n   j+=i\n primesd={}\n primesl = []\n for i in range(2, n+1):\n  if l[i]:\n   primesd[i]=True\n   primesl.append(i)\n return primesd, primesl\n\nprimesd, primesl = sieve(10000)\npc = [0]*10001 # pc:- pair count\n\n# pre-computing the counts for fast retreival\nfor e in primesl:\n for f in primesl:\n  temp = e+2*f\n  if temp > 10000:\n   break\n  pc[temp]+=1\n\nt =int(input())\n\nfor __ in range(t):\n n = int(input())\n print(pc[n])\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 180341