Kujou Karen is a girl with superpowers, but her powers can only be used for some strange things.

One day, Karen obtained a sequence $a_1, a_2, \dots, a_n$. She can use her superpower once on this sequence: 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 $a_l, a_{l+1}, \dots, a_r$ in the interval.

Kujou Karen likes sequences that are relatively consistent, so she wants the frequency of the mode in the final sequence to be as large as possible. Given the sequence $a$, you need to output the maximum possible frequency of the mode in the final sequence, and all possible values of this mode. Note that for a sequence, there may be more than one value that is a mode.

Input

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 $a_1, a_2, \dots, a_n$.

Output

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

Suppose there are $k$ different possible values for this mode. Output these values in increasing order on the next $k$ lines.

Constraints

For all test cases: $1 \le T \le 20$, $2 \le n \le 200\,000$, $1 \le a_i \le 10^9$. It is guaranteed that $\sum n \le 500\,000$ and that not all $a_i$ are equal.

The specific constraints for each test case are as follows: