382. Cantor Function

Time limit per test: 0.25 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard





The Cantor function f(x) (see picture) is defined as the function on [0, 1] as follows:

  • If x belongs to Cantor set ( where ni are different positive integers), then .
  • f is continuous and monotonous function.

    In 2004, Gorin and Kukushkin showed that is rational. You are to find In and output it as irreducible fraction.

    Input
    First line contains one integer number n (0 ≤ n ≤ 50).

    Output
    You should output In in the form p/q, where p and q are the numerator and the denominator of In respectively. Note that p and q must be natural and (p, q) must be equal to 1. You should output p and q without leading zeroes.

    Example(s)
    sample input
    sample output
    0
    
    1/1
    

    sample input
    sample output
    1
    
    1/2
    

    sample input
    sample output
    2
    
    3/10
    




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