Palindromic Doubles
Description
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 $a$?
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 $250\,000$.
For each testcase print a single integer — the length of the longest palindromic subsequence of sequence $a$.
Input
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
For each testcase print a single integer — the length of the longest palindromic subsequence of sequence $a$.
Samples
5
6
2 1 3 1 5 2
6
1 3 3 4 4 1
1
1
2
1 1
7
4 4 2 5 7 2 3
5
4
1
2
3
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