What's the missing column/row? (GCJ 2016-1A rankfile) There is an N x N square of numbers.


All columns increase strictly monotonically from top to down
All rows increase strictly monotonically from left to right
There is exactly one valid answer for each input.


You are given 2N-1 rows of N numbers representing rows or columns in this square. The task is to find the row that isn't in the input. 

Your Task
Write a program or function that outputs the row or column that isn't in the input.

Input

First, you get the number N.
Then follow 2N-1 lines of N space-separated numbers, representing rows or columns of this N x N square. The lines are given in left-to-right or top-down order. There may be multiple equal lines. It is ok to omit the initial N from the input, or modify the input format as you like. 

3
1 2 3
2 3 5
3 5 6
2 3 4
1 2 3


Output

Your program or function should output a single line of N numbers; the row or column from the square that was not present in the input. You may change the output format as you please.

3 4 6


This would correspond to one of two squares:

1 2 3     1 2 3
2 3 4     2 3 5
3 5 6     3 4 6


Either way, the output is the same.

Bonus

Your solution should be able to calculate 2 ≤ N ≤ 10 within a minute on a normal computer. If your solution handles the big input, 2 ≤ N ≤ 50, within a minute, you get -10% byte count.

Test cases

2
22 222
2 22
22 222
-&gt; 2 22


3
1 2 3
2 3 5
3 5 6
2 3 4
1 2 3
-&gt; 3 4 6

4
11 14 16 22
3 6 9 11
6 7 11 14
9 11 15 19
10 11 19 22
6 7 10 11
3 6 8 10
-&gt; 8 10 15 16


Note that you can simply change what line in these inputs that is omitted, and reorder them in any way you want, to generate new test cases. 

This is a simplified version of Google Code Jam 2016 round 1A problem B: Rank and File. The original Google Code Jam problem, where you can get more test cases (but without answers), is available here: https://code.google.com/codejam/contest/4304486/dashboard#s=p1
CJam, 5 - 10% = 4.5

This is an unnamed function (block) that takes an array of arrays and returns an array:

{:^$}


(With some inspiration from Dennis)

Try it online

And here is the code I actually submitted at GCJ (24 bytes):

li2*({l~}*]$e`{(2%*~}%S*


Try it online

Explanation:

This basically lists the values that appear an odd number of times.

:^    reduce by symmetric difference; pairs of duplicate values "cancel" each other
$     sort the resulting array