Problem Statement

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.

Constraints

• $2 ≤ N ≤ 10^5$
• $1 ≤ a_i ≤ N$

Input

Input is given from Standard Input in the following format:

N
a_1
a_2
:
a_N

Output

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 $2$.