zk has n numbers $a_1,a_2,...,a_n$. For each (i,j) satisfying 1=<i<j<=n,  zk generates a new number(ai+aj). . These new numbers could make up a new sequence b₁, b₂, ..., b_n(n-1)/2. LsF wants to make some trouble. While zk is sleeping, Lsf mixed up sequence a and b with random order so that zk can't figure out which numbers were in a or b. "I'm angry!", says zk.
Can you help zk find out which n numbers were originally in a?
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Multiple test cases(not exceed 10).
For each test case:
$\bullet$The first line is an integer m(0=<m<=125250), indicating the total length of a and b. It's guaranteed m can be formed as n(n+1)/2.
$\bullet$The second line contains m numbers, indicating the mixed sequence of a and b.
Each $a_i$ is in [1,10^9]

For each test case, output two lines.
The first line is an integer n, indicating the length of sequence a;
The second line should contain n space-seprated integers $a_1,a_2,...,a_n(a_1=<a_2<=...<=a_n)$. These are numbers in sequence a.
It's guaranteed that there is only one solution for each case.