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B - Trained?

Score : $200$ points

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 $2$.

3
3
1
2

2

Press Button $1$, then Button $3$.

4
3
4
1
2

-1

Pressing Button $1$ lightens up Button $3$, and vice versa, so Button $2$ will never be lighten up.

5
3
3
4
2
4

3