Problem H
Additive Primes
A prime number is an integer $n$ ($n \ge 2$) such that $n$ cannot be formed as the product of two other integers smaller than $n$. In other words, a number is prime if its factors are only one and itself. An integer which is greater than $2$ and is not prime is called a composite number.
An additive prime in base-$10$ is a number which is both prime and the sum of its digits forms a prime number. For example, $23$ is an additive prime, since $23$ is prime, and $2 + 3 = 5$ is also prime, but $13$ is not, since $1 + 3 = 4$, and $4$ is not prime.
Input
Input consists of a single integer $n$ ($2 \le n \le 2^{31} - 1$).
Output
Output “ADDITIVE PRIME” if the number is an additive prime. Output “PRIME, BUT NOT ADDITIVE” if the number is prime, but not an additive prime. Output “COMPOSITE” otherwise.
| Sample Input 1 | Sample Output 1 |
|---|---|
61 |
ADDITIVE PRIME |
| Sample Input 2 | Sample Output 2 |
|---|---|
17 |
PRIME, BUT NOT ADDITIVE |
| Sample Input 3 | Sample Output 3 |
|---|---|
141 |
COMPOSITE |
