G. Positivity
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

Egor has an array $$$a_1,a_2,...,a_n$$$ of integers and a permutation $$$p_1,p_2,...,p_n$$$ with $$$i \neq p_i$$$ for all $$$i$$$.

Egor is all about good vibes! He wants to make $$$a_i + a_{p_i}$$$ nonnegative for all $$$i$$$ after applying at most $$$\lfloor \frac{n}{2} \rfloor$$$ operations. In one operation, he will choose $$$x$$$ and negate both $$$a_x$$$ and $$$a_{p_x}$$$.

Help Egor choose the operation sequence!

Input

$$$n \\ a_1 \ a_2 \ \ldots \ a_n \\ p_1 \ p_2 \ \ldots \ p_n$$$

Constraints

$$$n \le 2 \cdot 10^5 \\ |a_i| \le 10^9$$$

Output

$$$x_1 \ x_2 \ \ldots \ x_n$$$

$$$x_i$$$ is the $$$i$$$-th choice of $$$x$$$

Examples
Input
4
3 -4 5 -6
2 1 4 3
Output
2
2 4
Input
6
1 -2 1 -2 1 -2
2 3 4 5 6 1
Output
3
2 3 6