A9685 | Misha and Permutations Summation

Let's define the sum of two permutations $p$ and $q$ of numbers $0,1,...,(n-1)$ as permutation , where $Perm(x)$ is the $x$ -th lexicographically permutation of numbers $0,1,...,(n-1)$ (counting from zero), and $Ord(p)$ is the number of permutation $p$ in the lexicographical order.

For example, $Perm(0)=(0,1,...,n-2,n-1)$ , $Perm(n!-1)=(n-1,n-2,...,1,0)$

Misha has two permutations, $p$ and $q$ . Your task is to find their sum.

Permutation $a=(a_{0},a_{1},...,a_{n-1})$ is called to be lexicographically smaller than permutation $b=(b_{0},b_{1},...,b_{n-1})$ , if for some $k$ following conditions hold: $a_{0}=b_{0},a_{1}=b_{1},...,a_{k-1}=b_{k-1},a_{k}<b_{k}$ .

The first line contains an integer $n$ ( $1<=n<=200000$ ).

The second line contains $n$ distinct integers from $0$ to $n-1$ , separated by a space, forming permutation $p$ .

The third line contains $n$ distinct integers from $0$ to $n-1$ , separated by spaces, forming permutation $q$ .

Print $n$ distinct integers from $0$ to $n-1$ , forming the sum of the given permutations. Separate the numbers by spaces.