Taco's Candy Chain

You are given n distinct candy pieces, each with a sweetness level. Your task is to arrange these candy pieces in a chain such that:

• The total sweetness of the chain, \(S = s_1 + s_2 + \cdots + s_n\), is even.
• For every three consecutive candy pieces in the chain, the sum of their sweetness levels is not divisible by 3. In other words, for every \(i\) with \(1 \le i \le n-2\), \[ s_i + s_{i+1} + s_{i+2} \not\equiv 0 \pmod{3}. \]

If such an arrangement exists, print any one valid ordering; otherwise, print -1.

Note: All candy pieces have distinct sweetness levels.

inputFormat

Input is read from standard input (stdin). The first line contains a single integer n denoting the number of candy pieces. The second line contains n space-separated integers representing the distinct sweetness levels of each candy piece.

outputFormat

If a valid arrangement exists, output a single line with n space-separated integers corresponding to a valid candy chain. If no valid arrangement exists, output -1.## sample

4
3 1 7 5

3 1 7 5