Beerus needs to sort an array of $N$ integers. Algorithms are not Beerus's strength. Destruction is what he excels. He can destroy all unsorted numbers in the array simultaneously. A number $A[i]$ of the array is sorted if it satisfies the following requirements. 1. $A[i]$ is the first element of the array, or it is no smaller than the left one $A[i-1]$. 2. $A[i]$ is the last element of the array, or it is no bigger than the right one $A[i+1]$. In $[1,4,5,2,3]$, for instance, the element $5$ and the element $2$ would be destoryed by Beerus. The array would become $[1,4,3]$. If the new array were still unsorted, Beerus would do it again. Help Beerus predict the final array.
The first line of input contains an integer $T~(1\le T\le 10)$ which is the total number of test cases. For each test case, the first line provides the size of the inital array which would be positive and no bigger than $100000$. The second line describes the array with $N$ positive integers $A,A,\cdots,A[N]$ where each integer $A[i]$ satisfies $1\le A[i]\le 100000$.
For eact test case output two lines. The first line contains an integer $M$ which is the size of the final array. The second line contains $M$ integers describing the final array. If the final array is empty, $M$ should be $0$ and the second line should be an empty line.