-----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 = '# calculate primes\ndef calcPrimes(tot):\n fin = []\n primes = [1]*(tot+1)\n start = 2\n\n while start < tot+1:\n  fin.append(start)\n  \n  # mark all factors of the given number      \n  for i in range(2*start,tot+1,start):\n   primes[i] = 0\n\n  start +=1\n  # check next unmarked number\n  while start < len(primes) and primes[start] == 0:\n   start += 1\n return fin\n\nprimes = calcPrimes((10**4)+5)\ncount = [0]*((10**4)+5)\n\n# mark possibility for each pair\nfor i in primes:\n for j in primes:\n  if (i+(2*j)) < len(count):\n   count[(i+(2*j))] += 1\n\nn = int(input())\nfor _ in range(n):\n print(count[int(input())])\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 143455