Odd Catalan numbers

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!”.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:52:06.136Z