#600 Longest Common Subsequence

Statement

Statement language

You are given a sequence $A=[A_1,A_2,\cdots,A_N]$ of length $N$ and a sequence $B=[B_1,B_2,\cdots,B_M]$ of length $M$ .

Print any longest common subsequence of $A$ and $B$ . A subsequence is obtained by deleting zero or more elements from a sequence while preserving the order of the remaining elements.

Input

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

Output

For each case, print the length $K$ of a longest common subsequence on one line. If $K>0$ , print its $K$ elements separated by spaces on the next line. If $K=0$ , print no elements.

If several longest common subsequences exist, you may print any of them.

Constraints

$1\leq T\leq100\,000$ .
$1\leq N,M\leq2000$ .
().

Subtasks

#	Score	Constraints
1	20	$N,M\leq8$ . The sum of $N+M$ over all cases is at most $2000$ . The sum of over all cases is at most .

Samples

Input

Output