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E. Minimum Array

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$j$$$ ($$$1 \le j < i$$$) $$$x_j = y_j$$$.

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 $$$c_i = (a_i + b_i) \% n$$$.

Examples

Input

4 0 1 2 1 3 2 1 1

Output

1 0 0 2

Input

7 2 5 1 5 3 4 3 2 4 3 5 6 5 1

Output

0 0 0 1 0 2 4

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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