D. Trivial Conjecturetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputf(n) = \left\{ \begin{array}{ll} \frac{n}{2} & n \equiv 0 \pmod{2}\\ 3n+1 & n \equiv 1 \pmod{2}\\ \end{array} \right.Find an integer n so that none of the first k terms of the sequence n, f(n), f(f(n)), f(f(f(n))), \dots are equal to 1.InputThe only line contains an integer k (1 \leq k \leq \min(\textbf{[REDACTED]}, 10^{18})).OutputOutput a single integer n such that none of the first k terms of the sequence n, f(n), f(f(n)), f(f(f(n))), \dots are equal to 1.Integer n should have at most 10^3 digits.ExamplesInput
1
Output
5Input
5
Output
6NoteIn the first test, the sequence created with n = 5 looks like 5, 16, 8, 4, 2, 1, 4, \dots, and none of the first k=1 terms are equal to 1.In the second test, the sequence created with n = 6 looks like 6, 3, 10, 5, 16, 8, 4, \dots, and none of the first k=5 terms are equal to 1.
1

5
['*special problem', 'constructive algorithms', 'math', 'number theory']