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?

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?

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:

$\bullet$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]

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