Problem Description

Mahsa has been practicing shuffling cards for a few months now. Tonight, she finally decided to invite her friends over and show off her new skills. So she picks up a deck with $2n$ cards, shows her friends the face of the cards without changing the deck order and asks someone to pick two positions $i$ and $j$ in the deck. Then, she tells everyone that she is going to move the card in the $i$-th position to the $j$-th position by applying only two types of shuffles.

Assume the cards in the deck are $\langle c_{1}, c_{2}, \ldots, c_{2n} \rangle$. Mahsa can perform these two shuffles as many times as she wants:

• Riffle: Divide the cards into two parts $\langle c_{1}, \ldots, c_{n} \rangle$ and $\langle c_{n+1}, \ldots, c_{2n} \rangle$ and produce $\langle c_{1}, c_{n+1}, c_{2}, c_{n+2}, \ldots, c_{n}, c_{2n} \rangle$.
• Scuffle: From $\langle c_{1}, c_{2}, \ldots, c_{2n} \rangle$, produce $\langle c_{2}, c_{1}, c_{4}, c_{3}, \ldots, c_{2n}, c_{2n-1} \rangle$.

Help Mahsa find out the minimum number of shuffles she needs, and she'll figure out the rest.

Input Format

The input consists of a single line containing three space-separated integers $n$, $i$ and $j$ ($1 \leq n \leq 10^{5}$ and $1 \leq i, j \leq 2n$).

Output Format

Print a single integer, the minimum number of shuffles required to bring the $i$-th card to $j$-th position. If it is not possible to do so, print $-1$ instead.

4 3 8

3

5 4 1

5

1 1 1 

0