Odd Catalan numbers P75985

The famous Catalan numbers can be defined by the recurrence $$C_n = \sum_{i=0}^{n-1} C_i \cdot C_{n-i-1} \enspace ,$$ with $C_0 = 1$. The first Catalan numbers are 1, 1, 2, 5, 14, 42, 132, …

You are given an index $i$. What is the smallest $j$ such that $j \ge i$ and $C_j$ is odd?

Input

Input consists of several cases, each with a natural number no larger than $10^{15}$.

Output

For every $i$, print the smallest $j$ such that $j \ge i$ and $C_j$ is odd. If such a number does not exist, print “Catalans are strange!”.