Polycarp studies in Berland State University. Soon he will have to take his exam. He has to pass exactly $n$ exams.

For the each exam $i$ there are known two days: $a_i$ — day of the first opportunity to pass the exam, $b_i$ — day of the second opportunity to pass the exam ($a_i < b_i$). Polycarp can pass at most one exam during each day. For each exam Polycarp chooses by himself which day he will pass this exam. He has to pass all the $n$ exams.

Polycarp wants to pass all the exams as soon as possible. Print the minimum index of day by which Polycarp can pass all the $n$ exams, or print -1 if he cannot pass all the exams at all.