Restoring a Permutation

You are given a positive integer $n$ and two arrays $a$ and $b$ containing $n$ integers each.

You need to find a permutation $p$ of length $n$ such that for each $i \in \{1, 2, \ldots, n\}$ the following two conditions are satisfied:

• the length of the longest increasing subsequence of $p$ ending at position $i$ is equal to $a_i$,
• the length of the longest decreasing subsequence of $p$ starting at position $i$ is equal to $b_i$.

The first line of input contains a positive integer $n$ ($1 \le n \le 2 \cdot 10^5$), the length of the permutation.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$, where $a_i$ is the length of the longest increasing subsequence ending at position $i$ ($1 \le a_i \le n$).

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$, where $b_i$ is the length of the longest decreasing subsequence starting at position $i$ ($1 \le b_i \le n$).

Print a line containing $n$ space-separated integers $p_1, p_2, \ldots, p_n$: the desired permutation.

It is guaranteed that the answer exists. If there are multiple solutions, you may print any one of them.