Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
Home Page
F.A.Qs
Statistical Charts
Problems
Submit Problem
Online Status
Prob.ID:
Register
Update your info
Authors ranklist
Current Contest
Past Contests
Scheduled Contests
Award Contest
User ID:
Password:
  Register
Language:
Children's Dining
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 4626Accepted: 719Special Judge

Description

Usually children in kindergarten like to quarrel with each other. This situation annoys the child-care women. For instant, when diner time comes, a fierce conflict may break out when a certain couple of children sitting side by side who are hostile with each other. Although there aren't too many children dining at the same round table, but the relationship of "enemy" or "friend" may be very complex. The child-care women do come across a big problem. Now it is time for you to help them to figure out a proper arrangement of sitting, with which no two "enemy" children is adjacent.

Now we assume that there are 2 * n children who sit around a big table, and that none has more than n - 1 "enemies".

Input

The input is consisted of several test blocks. For each block, the first line contains two integers n and m (1 <= n <= 200, 0 <= m <= n (n - 1)). We use positive integers from 1 to 2 * n to label the children dining round table. Then m lines followed. Each contains positive integers i and j ( i is not equal to j, 1 <= i, j <= 2 * n), which indicate that child i and child j consider each other as "enemy". In a input block, a same relationship isn't given more than once, which means that if "i j" has been given, "j i" will not be given.

There will be a blank line between input blocks. And m = n = 0 indicates the end of input and this case shouldn't be processed.

Output

For each test block, if the proper arrangement exist, you should print a line with a proper one; otherwise, print a line with "No solution!".

Sample Input

1 0

2 2
1 2
3 4

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

4 12
1 2
1 3
1 4
2 5
2 6
3 7
3 8
4 8
4 7
5 6
5 7
6 8

0 0

Sample Output

1 2
4 2 3 1
1 6 3 2 5 4
1 6 7 2 3 4 5 8

Source

POJ Monthly,anonymous

[Submit]   [Go Back]   [Status]   [Discuss]

Home Page   Go Back  To top


All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di
Any problem, Please Contact Administrator