Problem Description

Given an odd prime p.
You are to tell whether p can be written into form a^2+b^2 (0<a<=b),
and if p can be done, you are to determine a pair of a,b.

Input

There will be up to 2*10^5 test cases.
An odd prime p (3<=p<2*10^9) in each line.
End with EOF.

Output

For each number p,
if p can be written into form a^2+b^2 (0<=b),
output one line that contains "Legal a b",
and if not just output one line that contains "Illegal".
For a certain p that can be written into the form described above, any pair of a,b (0<=b) will do.

3
5
7
11
13
17
19
23
29

Illegal
Legal 1 2
Illegal
Illegal
Legal 2 3
Legal 1 4
Illegal
Illegal
Legal 2 5