Your teacher wrote a sequence of ~N~ distinct integers on the board, the homework questions you are supposed to solve for the next class. The ~i^\text{th}~ of these integers is ~a_i~. However, while your teacher wasn't looking, your mischievous friend erased all ~N~ numbers and replaced them with a new sequence consisting of the sum of every ordered pair of elements in the original sequence. The ~i^\text{th}~ integer in the new sequence is ~b_i~. As a good student, you would like to do your homework questions. Write a program that, given the modified sequence, recovers the initial sequence.

Constraints

~1 \le N \le 100~

~1 \le a_i, b_i \le 10^9~

Subtask 1 [10%]

~N = 2~

Subtask 2 [10%]

~N = 3~

Subtask 3 [80%]

No additional constraints.

Input Specification

The first line contains a single integer, ~N~, the length of the initial sequence.

The second line contains ~N^2~ integers, ~b_i~, the elements of the modified sequence.

Output Specification

Output a single line containing ~N~ space-separated integers, the initial sequence.

You should output the integers in increasing order.

If there are several solutions, you may output any one of them.

Sample Input

2
5 4 5 6

Sample Output

2 3