Problem Description

Kurenai Kujou is a pitiful girl with superpowers, but her superpower can only be used on some strange things.

One day, Kurenai got a sequence $a_1, a_2, \ldots, a_n$. She can use her superpower on this sequence once: choose an interval $[l, r]$ ($1 \le l \le r \le n$) and an integer $k \in [-{10}^9, {10}^9]$, and add $k$ to all numbers $a_l, a_{l + 1}, \ldots, a_r$ in the interval.

Kurenai likes sequences that look as consistent as possible, so she wants the final sequence to have the mode occur as many times as possible. Given the sequence $a$, you need to output the maximum possible number of occurrences of the mode in the final sequence, and output all possible values of this mode. Note that for a sequence, the mode may have more than one value.

Input Format

The input contains multiple test cases. The first line contains the number of test cases $T$.

For each test case, the first line contains the sequence length $n$, and the second line contains $n$ integers $a_1, a_2, \ldots, a_n$.

Output Format

For each test case, output the maximum possible number of occurrences of the mode in the final sequence on the first line.

Suppose this mode has $k$ different possible values. Then output these values in increasing order, one per line, for a total of $k$ lines.

4
5
1 2 3 2 1
5
1 1 3 1 1
6
2 4 2 4 8 8
5
1 2 3 4 5

4
1
5
1
4
2
4
8
2
1
2
3
4
5

见附件中的 mode/mode_ex2.in

见附件中的 mode/mode_ex2.ans

Hint

For all testdata: $1 \le T \le 20$, $2 \le n \le 2 \times {10}^5$, $1 \le a_i \le {10}^9$, it is guaranteed that $\sum n \le 5 \times {10}^5$, and the $a_i$ are not all equal.

The specific limits for each test point are shown in the table below:

Translated by ChatGPT 5