Bilateral Projects 
Problem ID: bilateral

A friend of yours works at an undisclosed company in the music streaming industry, 
and needs your help. The company has offices in Stockholm and London, and 
collaboration between the two offices is extensive. The situation is that each of
the many but small projects is handled by a two-person team with a member in each
city. While emails, faxes, and phones are wonderful, and work well within each team,
the CEO wants a briefing every year on the projects. For this purpose the CEO
invites representatives from the projects to Barbados for a week of beach fun 
presentations of all the projects. However, money is tight and a new policy has 
been created: the CEO wants at least one person from each project, and additionally, 
she wants to invite as few people as possible. This is where you come in. In order 
to help your friend get a ticket to Barbados, you are to write a program that, 
given all the two-person teams, computes the smallest number of people that must 
be invited in order to get at least one person from each project, as well as a 
list of people to invite. If possible (subject to the set of people being smallest 
possible), the list of invitees should include your friend.

Input:
The first line of input contains an integer 1 ! m ! 10 000, the number of teams. 
The following m lines each contain two integers, i, j separated by a space, being 
the employee IDs of the two employees in that team (the first one is from Stockholm 
and the second one is from London). Stockholm employees have IDs in the range 1000 
to 1999 and London employees have IDs in the range 2000 to 2999. An employee can be 
a member of several teams, but there cannot be several teams consisting of the same 
pair of employees. Y our friend has ID 1009.

Output:
Output first a single line with an integer k indicating the smallest number of 
employees that must be invited to meet the requirements above. Then output k lines
giving the IDs of employees to invite. If possible (subject to k being smallest
possible), the list should contain your friend. 

If there are several solutions subject to these constraints, anyone is acceptable.

Sample input 1
2
1009 2011 
1017 2011 

Sample output 1 
1
2011 

Sample input 2
4 
1009 2000 
1009 2001 
1002 2002 
1003 2002 

Sample output 2
2 
2002 
1009