Trained?

AtCoder

IDabc065_b

Time2000ms

Memory256MB

Difficulty—

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: $N$ $a_1$ $a_2$ : $a_N$ [samples]

Samples

Input #1

Output #1

2

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

Input #2

Output #2

\-1

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

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Trained?",
    "description": {
      "content": "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 $1$ th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc065_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi wants to gain muscle, and decides to work out at AtCoder Gym.\nThe exercise machine at the gym has $N$ buttons, and exactly one of the buttons is lighten up. These buttons are numbered $1$ th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments