Shortest Thue-Morse String Length

In this problem, you are given an integer ( n ) (with ( 1 \le n \le 10^5 )). The task is to determine the length of the shortest Thue-Morse string that can be constructed such that its length is at least ( n ). The Thue-Morse string is generated iteratively where starting with "0", each subsequent iteration appends the binary complement of the string so far. Notice that the length of the Thue-Morse string is always a power of 2. Therefore, the answer is simply the smallest power of ( 2 ) that is greater than or equal to ( n ).

inputFormat

The input consists of a single integer ( n ) provided via standard input.

outputFormat

Output the length of the shortest Thue-Morse string (a power of 2) that is at least ( n ), via standard output.## sample

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