O Fortuna

Time limit1sMemory limit1024 MB

Summary

Given N, compute P as the product of the first N primes, then output Q minus P (Q is the next prime above P+1) and P minus Q (Q is the previous prime below P-1).

Level: Medium4 of 10
Topics: Number theory, Implementation
Solved: No attempts yet

Problem

Some numbers in mathematics are fortunate, and others are less fortunate. A fortunate number is $Q - P$ , where $P$ is the product of the first $N$ prime numbers ( $N > 1$ ), and $Q$ is the smallest prime greater than $P + 1$ . For example, with $N = 2$ , $P = 2 \times 3 = 6$ . The smallest prime greater than 7 is 11, so the fortunate number is $11 - 6 = 5$ , which is also prime. Some mathematicians have conjectured that fortunate numbers are always prime.

A less fortunate number is $P - Q$ , using the same $P$ , except that $Q$ is the largest prime less than $P - 1$ . With $N = 2$ , $P = 6$ , so $Q = 3$ (the largest prime less than 5), and the less fortunate number is $6 - 3 = 3$ . A similar conjecture says that less fortunate numbers are always prime.

Input

A single integer $N$ with $1 < N \leq 14$ .

Output

Print the input value $N$ , followed by the fortunate number and the less fortunate number as described above. Separate each output item with a single space.

Examples1

Example 1

Input

2 3 4

Expected output

N = 2 FORTUNATE = 5 LESS = 3
N = 3 FORTUNATE = 7 LESS = 7
N = 4 FORTUNATE = 13 LESS = 11