18636번 - Restoring a Permutation 스페셜 저지다국어

문제

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

You need to find permutation p of length n such that for each i ∈ {1, 2, . . . , n} the following two conditions are satisfied:

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

입력

The first line of input contains a positive integer n (1 ≤ n ≤ 2 · 10⁵), the length of the permutation.

The second line contains n integers a₁, a₂ . . . , a_n, where a_i (1 ≤ a_i ≤ n): the length of longest increasing subsequence ending at position i.

The third line contains n integers b₁, b₂ . . . , b_n, where b_i (1 ≤ b_i ≤ n): the length of longest decreasing subsequence starting at position i.

출력

Print a line containing n space-separated integers p₁, p₂, . . . , p_n: the desired permutation.

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

제한

힌트