Numbers

Time Limit: 4000/2000 MS (Java/Others)

Memory Limit: 131072/131072 K (Java/Others)

Description

zk has n numbers $a_1,a_2,...,a_n$. For each (i,j) satisfying 1≤i<j≤n, zk generates a new number $(a_i+a_j)$. These new numbers could make up a new sequence $b_1,b_2, ... ,b_{n(n-1)/2}$.
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?

Input

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]

Output

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.

Sample Input

6 2 2 2 4 4 4 21 1 2 3 3 4 4 5 5 5 6 6 6 7 7 7 8 8 9 9 10 11

Sample Output

3 2 2 2 6 1 2 3 4 5 6

Hint

liuyiding

Source

2017 Multi-University Training Contest - Te

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