시간 제한 | 메모리 제한 | 제출 | 정답 | 맞힌 사람 | 정답 비율 |
---|---|---|---|---|---|
2 초 | 512 MB | 25 | 17 | 17 | 68.000% |
Christina has a rooted tree with $n$ vertices. Initially, all vertices are colored green, except for the root, which is colored red. Christina thinks that the tree is beautiful if two rules are satisfied:
Christina repeatedly performs the following operation on the tree --- chooses a vertex and changes its color (if it was red, colors it green; if it was green, colors it red). The following rules must be satisfied while performing the operations:
Your task is to help Christina build the longest possible sequence of operations following the rules.
The first line contains an integer $n$ ($1 \le n \le 20$) --- the number of vertices in the tree.
The second line contains $n - 1$ integers $p_i$ ($1 \le p_i \le i$ for $1 \le i \le n - 1$), denoting parent vertices in the tree. The vertices in the tree are numbered from $1$ to $n$, the root has number $1$, the $i$-th vertex has parent $p_{i-1}$ for $2 \le i \le n$.
On the first line output an integer $m$ --- the maximum number of operations.
On the second line output $m$ integers $o_i$ ($2 \le o_i \le n)$. $o_i$ is the number of the vertex that changes color during the corresponding operation.
If there are several possible longest sequences, output any one of them.
4 1 1 1
7 4 3 4 2 4 3 4
4 1 2 3
3 2 3 4
6 1 1 2 2 2
17 3 2 3 6 3 5 3 6 3 4 3 6 3 5 3 6 3
5 1 2 1 1
11 5 4 5 2 5 4 5 3 5 4 5
5 1 1 2 3
8 3 5 2 5 3 4 3 5