Problem Statement

There is a huge kusunoki (camphor tree) in front of the clock tower of Kyoto University. It is reported that this kusunoki has the following structure.

• There exists a positive integer $N$ and the kusunoki has $2^N-1$ branch points, which are numbered from $1$ to $2^N-1$.
• For each integer $i$ that holds $1 \leq i \leq 2^{N-1}-1$, the kusunoki has branches according to the following rules.
  • Branch point $i$ and $2i$ are connected with a branch.
  • Branch point $i$ and $2i + 1$ are connected with a branch.
• There is no branch that does not hold the above rules.

For example, for $N=3$, the structure of the kusunoki is as follows.

Kusunoki $N=3$

You want to climb this kusunoki. You can climb from branch point $S$ to $T$ if and only if $S=T$ or there exists a path of branches from $S$ to $T$, where the numbers of branch points are in ascending order from $S$ to $T$. Given two integers $S$ and $T$, determine whether you can climb from branch point $S$ to $T$. Also, if it is possible, answer the lowerst number of branches you need to climb.

Constraints

• $1 \leq N \leq 25$
• $1 \leq S \leq 2^N-1$
• $1 \leq T \leq 2^N-1$
• $N,S,T$ are integers.

Sample Input 1Copy

3 2 4

Sample Output 1Copy

1

Since you can climb from branch point $2$ to $4$ through one branch, print 1.

Sample Input 2Copy

3 7 1

Sample Output 2Copy

-1

Sample Input 3Copy

4 2 2

Sample Output 3Copy

0