In number theory there is a very deep unsolved conjecture of the Hungarian Paul Erdős (1913-1996), that there exist infinitely many primes of the form x²+1, where x is an integer. However, a weaker form of this conjecture has been proved: there are infinitely many primes of the form x²+y⁴. You don't need to prove this, it is only your task to find the number of (positive) primes not larger than n which are of the form x²+y⁴ (where x and y are integers).

Input

An integer T, denoting the number of testcases (T≤500000). Each of the T following lines contains a positive integer n, where n ≤ 10¹².

Output

Output the answer for each n.

Example

Input:
6
1
2
10
9999999
500000000000
1000000000000

Output:
0
1
2
13175
25874902
42377120

ps. my running time on Cube is 9.83 seconds. There is one input set.

For a much easier version of this problem see HS08PAUL.