COCI 2008/2009, Contest #6

Task CUSKIJA

Rearrange the given array of integers so that the sum of two adjacent elements is never divisible by three.

Input

The first line contains an integer N (1 ≤ N ≤ 10,000), the number of elements in the array.
The second line contains the elements of the array separated by single spaces. The elements will be positive integers less than 1,000,000.

Output

If any valid rearrangement exists, output it on a single line. Otherwise, output "impossible".

Examples

Input 3 1 2 3 Output 2 3 1

Input 5 4 6 3 9 8 Output 3 4 6 8 9

Input 6 3 7 6 4 2 8 Output 3 7 4 6 2 8

Input 3 3 12 9 Output impossible

All Submissions
Best Solutions

Point Value: 10
Time Limit: 1.00s
Memory Limit: 32M
Added: Mar 09, 2009

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

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