Trivial Conjecture

Description:

Input:

The only line contains an integer $$$k$$$ ($$$1 \leq k \leq \min(\textbf{[REDACTED]}, 10^{18})$$$).

Output:

Output 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.

Sample Input:

1

Sample Output:

5

Sample Input:

5

Sample Output:

6

Note:

In 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 $$$1$$$.