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