You are given an integer sequence $a_1, a_2, \ldots, a_n$. Let $S$ be the set of all possible non-empty subsequences of $a$ without duplicate elements. Your goal is to find the longest sequence in $S$. If there are multiple of them, find the one that minimizes lexicographical order after multiplying terms at odd positions by $-1$.

For example, given $a = [3, 2, 3, 1]$, $S = \{[1], [2], [3], [2, 1], [2, 3], [3, 1], [3, 2], [2, 3, 1], [3, 2, 1]\}$. Then $[2, 3, 1]$ and $[3, 2, 1]$ would be the longest, and $[3, 2, 1]$ would be the answer since $[-3, 2, -1]$ is lexicographically smaller than $[-2, 3, -1]$.

A sequence $c$ is a subsequence of a sequence $d$ if $c$ can be obtained from $d$ by the deletion of several (possibly, zero or all) elements.

A sequence $c$ is lexicographically smaller than a sequence $d$ if and only if one of the following holds:

• $c$ is a prefix of $d$, but $c \ne d$;
• in the first position where $c$ and $d$ differ, the sequence $c$ has a smaller element than the corresponding element in $d$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 5 \cdot 10^4$). The description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \le n \le 3 \cdot 10^5$) — the length of $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$) — the sequence $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $3 \cdot 10^5$.

Output

For each test case, output the answer in the following format:

Output an integer $m$ in the first line — the length of $b$.

Then output $m$ integers $b_1, b_2, \ldots, b_m$ in the second line — the sequence $b$.

Note

In the first example, $S = \{[1], [2], [3], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2], [2, 1, 3], [3, 2, 1]\}$. Among them, $[2, 1, 3]$ and $[3, 2, 1]$ are the longest and $[-3, 2, -1]$ is lexicographical smaller than $[-2, 1, -3]$, so $[3, 2, 1]$ is the answer.

In the second example, $S = \{[1]\}$, so $[1]$ is the answer.