Score : $200$ points
Takahashi wants to gain muscle, and decides to work out at AtCoder Gym.
The exercise machine at the gym has $N$ buttons, and exactly one of the buttons is lighten up. These buttons are numbered $1$ through $N$. When Button $i$ is lighten up and you press it, the light is turned off, and then Button $a_i$ will be lighten up. It is possible that $i=a_i$. When Button $i$ is not lighten up, nothing will happen by pressing it.
Initially, Button $1$ is lighten up. Takahashi wants to quit pressing buttons when Button $2$ is lighten up.
Determine whether this is possible. If the answer is positive, find the minimum number of times he needs to press buttons.
Input is given from Standard Input in the following format:
$N$ $a_1$ $a_2$ : $a_N$
Print $-1$ if it is impossible to lighten up Button $2$. Otherwise, print the minimum number of times we need to press buttons in order to lighten up Button $2$.
3 3 1 2
Press Button $1$, then Button $3$.
4 3 4 1 2
Pressing Button $1$ lightens up Button $3$, and vice versa, so Button $2$ will never be lighten up.
5 3 3 4 2 4