Minimum Array
Description
You are given two arrays $a$ and $b$, both of length $n$. All elements of both arrays are from $0$ to $n-1$.
You can reorder elements of the array $b$ (if you want, you may leave the order of elements as it is). After that, let array $c$ be the array of length $n$, the $i$-th element of this array is $c_i = (a_i + b_i) \% n$, where $x \% y$ is $x$ modulo $y$.
Your task is to reorder elements of the array $b$ to obtain the lexicographically minimum possible array $c$.
Array $x$ of length $n$ is lexicographically less than array $y$ of length $n$, if there exists such $i$ ($1 \le i \le n$), that $x_i < y_i$, and for any $j$ ($1 \le j < i$) $x_j = y_j$.
The first line of the input contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of elements in $a$, $b$ and $c$.
The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i < n$), where $a_i$ is the $i$-th element of $a$.
The third line of the input contains $n$ integers $b_1, b_2, \dots, b_n$ ($0 \le b_i < n$), where $b_i$ is the $i$-th element of $b$.
Print the lexicographically minimum possible array $c$. Recall that your task is to reorder elements of the array $b$ and obtain the lexicographically minimum possible array $c$, where the $i$-th element of $c$ is $c_i = (a_i + b_i) \% n$.
Input
The first line of the input contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of elements in $a$, $b$ and $c$.
The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i < n$), where $a_i$ is the $i$-th element of $a$.
The third line of the input contains $n$ integers $b_1, b_2, \dots, b_n$ ($0 \le b_i < n$), where $b_i$ is the $i$-th element of $b$.
Output
Print the lexicographically minimum possible array $c$. Recall that your task is to reorder elements of the array $b$ and obtain the lexicographically minimum possible array $c$, where the $i$-th element of $c$ is $c_i = (a_i + b_i) \% n$.
Samples
4
0 1 2 1
3 2 1 1
1 0 0 2
7
2 5 1 5 3 4 3
2 4 3 5 6 5 1
0 0 0 1 0 2 4