{"raw_statement":[{"iden":"problem statement","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 $1$ 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.\nInitially, Button $1$ is lighten up. Takahashi wants to quit pressing buttons when Button $2$ is lighten up.\nDetermine whether this is possible. If the answer is positive, find the minimum number of times he needs to press buttons."},{"iden":"constraints","content":"*   $2 ≤ N ≤ 10^5$\n*   $1 ≤ a_i ≤ N$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$a_1$\n$a_2$\n:\n$a_N$"},{"iden":"sample input 1","content":"3\n3\n1\n2"},{"iden":"sample output 1","content":"2\n\nPress Button $1$, then Button $3$."},{"iden":"sample input 2","content":"4\n3\n4\n1\n2"},{"iden":"sample output 2","content":"\\-1\n\nPressing Button $1$ lightens up Button $3$, and vice versa, so Button $2$ will never be lighten up."},{"iden":"sample input 3","content":"5\n3\n3\n4\n2\n4"},{"iden":"sample output 3","content":"3"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}