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 (10^5)
1 ≤ N ≤ 10000 (10^4)

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.

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