Description

Original source: USACO

Given the sums of the first $1$, first $2$, first $3$, $\cdots$, first $n$ terms, as well as the sums of the last $1$, last $2$, last $3$, $\cdots$, last $n$ terms of the original sequence $a_1, a_2, \cdots, a_n$, but all numbers have been shuffled. Additionally, we know that all elements in the sequence belong to the set $S$. The task is to reconstruct the original sequence. If multiple sequences are possible, output the lexicographically smallest one.

Input Format

Line $1$: An integer $n$.
Line $2$: $2 \times n$ integers, note: the data has been shuffled.
Line $3$: An integer $m$, the size of set $S$.
Line $4$: $m$ integers, representing the elements of set $S$.

Output Format

Output the lexicographically smallest sequence that satisfies the conditions.

Sample 1

5
1 2 5 7 7 9 12 13 14 14
4
1 2 4 5

1 1 5 2 5

Data Range and Hints

Data Range

For $100\%$ of the data, $1 \le n \le 1000$, $1 \le m \le 500$, and $S \subseteq \{1, 2, \cdots, 500\}$.

Sample Explanation