Problem:
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.

Sample Input 1

3
3
1
2

Sample Output 1

2

Press Button 1, then Button 3.

Sample Input 2

4
3
4
1
2

Sample Output 2

-1

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

Sample Input 3

5
3
3
4
2
4

Sample Output 3

3

Solution in Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val list = (1..n).map { readLine()!!.toInt() }
    val ans = solve(list)
    print(ans)
}

fun solve(nums: List<Int>): Int {
    val invalid = -1

    // 無限ループ構造
    // そもそも2が存在しない
    // 2のindexに紐づく値が存在しない
    val withIndex = nums.withIndex()
    return calculate(withIndex.toList(), 0, 0)
}

tailrec fun calculate(list: List<IndexedValue<Int>>, n: Int, index: Int?): Int {
    val a = list.firstOrNull { it.index == index }?.value

    return when {
        list.size == n -> {
            -1
        }
        a == null -> {
            -1
        }
        a == 2
        -> {
            n + 1
        }
        else -> {
            calculate(list, n + 1, a - 1)
        }
    }


}