CF279D The Minimum Number of Variables

You've got a positive integer sequence $ a_{1},a_{2},...,a_{n} $ . All numbers in the sequence are distinct. Let's fix the set of variables $ b_{1},b_{2},...,b_{m} $ . Initially each variable $ b_{i} $ $ (1

The first line contains integer $ n $ $ (1

In a single line print a single number — the minimum number of variables $ m $ , such that those variables can help you perform the described sequence of operations. If you cannot perform the sequence of operations at any $ m $ , print -1.

In the first sample, you can use two variables $ b_{1} $ and $ b_{2} $ to perform the following sequence of operations. 1. $ b_{1} $ := $ 1 $ ; 2. $ b_{2} $ := $ b_{1}+b_{1} $ ; 3. $ b_{1} $ := $ b_{1}+b_{2} $ ; 4. $ b_{1} $ := $ b_{1}+b_{1} $ ; 5. $ b_{1} $ := $ b_{1}+b_{2} $ .