1488E · Palindromic Doubles

Problem: A subsequence is a sequence that can be obtained from another sequence by removing some elements without changing the order of the remaining elements.

A palindromic sequence is a sequence that is equal to the reverse of itself.

You are given a sequence of $n$ integers $a_1, a_2, \dots, a_n$. Any integer value appears in $a$ no more than twice.

What is the length of the longest palindromic subsequence of sequence $a$?

Input Format: The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of testcases.

Then the descriptions of $t$ testcases follow.

The first line of each testcase contains a single integer $n$ ($1 \le n \le 250\,000$) — the number of elements in the sequence.

The second line of each testcase contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$).

Any integer value appears in $a$ no more than twice. The sum of $n$ over all testcases doesn't exceed $250\,000$.

Output Format: For each testcase print a single integer — the length of the longest palindromic subsequence of sequence $a$.

Note: Here are the longest palindromic subsequences for the example testcases:

• 2 1 3 1 5 2
• 1 3 3 4 4 1 or 1 3 3 4 4 1
• 1
• 1 1
• 4 4 2 5 7 2 3 or 4 4 2 5 7 2 3