Additive Primes

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시간 제한1초메모리 제한2048 MB

요약

정수 n이 주어질 때 n이 소수인지와 각 자리 숫자의 합이 소수인지를 판별해 해당 분류를 출력한다.

난이도: 쉬움10점 중 3점
유형: 수학, 정수론, 구현
정답자: 아직 제출이 없습니다

문제

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.

입력

Input consists of a single integer $n$ ( $2 \le n \le 2^{31} - 1$ ).

출력

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.

예제3

예제 1
입력
```
61
```
예상 출력
```
ADDITIVE PRIME
```
예제 2
입력
```
17
```
예상 출력
```
PRIME, BUT NOT ADDITIVE
```
예제 3
입력
```
141
```
예상 출력
```
COMPOSITE
```