Arcade Token Mismatch Pair

An arcade's coin-op machines are each stamped with a numeric machine ID. A maintenance log records, in order, the ID of the machine that fired every time it dispensed a token during a single business day. The shift manager suspects two specific machines are behaving inconsistently with each other and wants to flag the pair that is easiest to justify to a technician: the lexicographically smallest pair of distinct machine IDs appearing anywhere in the log whose total dispense counts for the day differ from one another.

Formally, count how many times each distinct machine ID occurs in the log. Among all pairs of distinct IDs (a, b) with a < b such that the count of a differs from the count of b, find the pair that is smallest when compared first by a, then by b, and report it. If every pair of distinct IDs has matching counts (including when at most one distinct ID appears in the log), report that no such pair exists.

Input format

• Line 1: a single integer n, the number of dispense events in the log.
• Line 2: n space-separated integers, the machine ID recorded for each event, in the order the events occurred.

Output format

• If a valid pair exists, print two space-separated integers a b (a < b): the lexicographically smallest pair of distinct machine IDs whose dispense counts differ.
• Otherwise, print -1 -1.

Constraints

• 1 <= n <= 500
• 1 <= id <= 1,000,000 for every recorded machine ID

5
4 2 4 2 5

2 5

3
7 7 7

-1 -1