Magic with Cards

문제

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 whithout 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 ⟨c₁, c₂, ..., c_2n⟩. Mahsa can perform these two shuffles as many times as she wants:

Riffle: Divide the cards into two parts⟨c₁, c₂, ..., c_n⟩ and ⟨c_n+1, ..., c_2n⟩ and produce ⟨c₁, c_n+1, c₂, c_n+2, ..., c_n, c_2n⟩.

Scuffle: From ⟨c₁, c₂, ..., c_2n⟩, produce ⟨c₂, c₁, c₄, c₃, ..., c_2n, c_2n-1⟩.

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

입력

The input consists of a single line containing three space-separated integers n, i and j (1 ⩽ n ⩽ 10⁵ and 1 ⩽ i, j ⩽ 2n).

출력

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