26505번 - O Fortuna 다국어

문제

In mathematics there are numbers that are fortunate, and some less fortunate. A fortunate number is defined as Q – P, where P is the product of the first N prime numbers (where N>1), and Q is the smallest prime greater than P+1. For example, if N = 2, P = 2*3 (the first two prime numbers), or 6. Q would be the smallest prime greater than 7, which is 11. Q – P is therefore 11 – 6, which is 5, another prime number. It has been conjectured by some mathematicians that this Fortunate number value will always be prime.

Likewise, a less fortunate number is defined as P – Q, using the same above scenario, except that Q is the largest prime less than P-1. Therefore, with N = 2, P again is 6, which makes Q = 3 (the largest prime less than 5), and so the LESS fortunate number in this case is 3. A similar conjecture for LESS fortunate numbers also asserts that they will always be prime.

입력

A row of integer values N in the range 1 < N <= 14.

출력

The original input value N, followed by the fortunate and less fortunate number, as described above, and shown below, with a single space separating each output item.

제한

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