Golden Primes

A prime number is called a golden prime when it takes the following form:

p = Φ² – Φ – 1,

where Φ = 2ⁿ, and n is a positive integer.

Your task is to find golden primes. Write a program that calculates all values for n for which p is a golden prime less than a given value b.

Input Specification

The input consists of a single positive integer b < 2¹⁰⁰⁰.

Output Specification

Your program must print to the standard output, on separate lines, all n values found.

Sample Input

1. 1024

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Output for Sample Input

1. 2
2. 4
3. 5

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