Problem A
RSA Mistake

An RSA number is a positive integer $n$ that is the product of two distinct primes. For example, $10=2\cdot 5$ and $77=7\cdot 11$ are RSA numbers whereas $7=7,9=3\cdot 3$, and $105=3\cdot 5\cdot 7$ are not.

You are teaching a course that covers RSA cryptography. For one assignment problem, you asked students to generate RSA numbers. They were to submit two positive integers $A,B$. Ideally, these would be distinct prime numbers. But some students submitted incorrect solutions. If they were not distinct primes, partial credit can be earned if $A\cdot B$ is not an integer multiple of $k^2$ for any integer $k\ge 2$. If there is an integer $k\ge 2$ such that $k^2$ divides $A\cdot B$, then the student receives no credit.

For a pair of positive integers submitted by a student for the assignment, determine if they should receive full credit, partial credit, or no credit for this submission.

Note: In the sixth sample case below, the number $545528636581\cdot 876571629707$ is divisible by $1000{003}^2$ and in the seventh sample case below, the number $431348146441\cdot 3$ is divisible by $656{771}^2$.

Input

The input consists of a single line containing two integers $A$ ($2\le A\le {10}^{12}$) and $B$ ($2\le B\le {10}^{12}$), which are the two submitted numbers.

Output

Display if the student should receive full credit, partial credit, or no credit for the submitted numbers.

13 23

full credit

35 6

partial credit

4 5

no credit

17 17

no credit

15 21

no credit

545528636581 876571629707

no credit

431348146441 3

no credit