Description

Given a sequence $a$ of length $n$, reorder it so that in the new sequence, the sum of any two adjacent numbers is not divisible by $3$.

Input Format

The first line contains an integer $n$, the length of the sequence.

The second line contains $n$ integers. The $i$-th integer is the $i$-th element of the sequence, $a_i$.

Output Format

This problem uses Special Judge.

• If a solution exists, output a string Yes on the first line, and on the second line output $n$ integers, where the $i$-th integer is the $i$-th element of the new sequence.
• If no solution exists, output only a string No on one line.

3
1 2 3

Yes
2 3 1

5
4 6 3 9 8

Yes
3 4 6 8 9

6
3 7 6 4 2 8

Yes
3 7 4 6 2 8

3
3 12 9

No

Hint

Constraints

For all testdata, it is guaranteed that $1 \leq n \leq 10^4$ and $1 \leq a_i \leq 10^6$.

[Notes]

This problem is translated from COCI2008-2009 CONTEST #6 T4 CUSKIJA. The translation and SPJ are provided by @一扶苏一. For easier SPJ checking, the output format is slightly modified compared to the original problem.

Translated by ChatGPT 5