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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

"use strict";

var main = function main(input) {
  var args = input.split('\n');
  var N = parseInt(args[0], 10);
  var a = [];

  for (var i = 1; i <= N; i++) {
    a.push(parseInt(args[i], 10));
  }

  var start = 1;
  var next = a[0];
  var checked = [];
  checked.push(1);
  var flag = false;
  var count = 0;

  while (next != start) {
    count++;
    next = a[next - 1];

    if (next == 2) {
      flag = true;
      break;
    }

    if (checked.indexOf(next) >= 0) {
      break;
    } else {
      checked.push(next);
    }
  }

  if (flag) {
    console.log(count + 1);
  } else {
    console.log(-1);
  }
};

main(require('fs').readFileSync('/dev/stdin', 'utf-8'));