• محدودیت زمان: ۱ ثانیه
• محدودیت حافظه: ۲۵۶ مگابایت

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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 \(\langle c_1, c_2, \dots, c_{2n} \rangle\). Mahsa can perform these two shuffles as many times as she wants:

Riffle: Divide the cards into two parts \(\langle c_1, \dots, c_n \rangle\) and \(\langle c_{n+1}, \dots, c_{2n} \rangle\) and produce \(\langle c_1, c_{n+1}, c_2, c_{n+2}, \dots, c_n, c_{2n} \rangle\).

Scuffle: From \(\langle c_1, c_2, \dots, c_{2n} \rangle\), produce \(\langle c_2, c_1, c_4, c_3, \dots, c_{2n}, c_{2n-1} \rangle\).

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

ورودی

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

خروجی

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

مثال‌ها

ورودی نمونه ۱

4 3 8

خروجی نمونه ۱

3

ورودی نمونه ۲

5 4 1

خروجی نمونه ۲

5

ورودی نمونه ۳

1 1 1

خروجی نمونه ۳

0