Robots

There are $N$ robots numbered from $1$ through $N$ and $N$ antennas numbered from $1$ through $N$ on a straight line. The coordinate of robot $i$ is $a_i$ and the coordinate of antenna $i$ is $b_i$. All coordinates are distinct.

Currently all antennas are inactive. You are going to activate them one by one. When you activate an antenna, the nearest robot moves to that antenna and explodes along with it. If two robots are equally close, only the left one moves.

Find an order to activate the antennas so that the total distance the robots move is minimum.

Input is given from Standard Input in the following format:

$N$

$a_1$ $a_2$ $\dots$ $a_N$

$b_1$ $b_2$ $\dots$ $b_N$

Print the answer in the following format:

$X$

$p_1$ $p_2$ $\dots$ $p_N$

Here, $X$ is the minimum total distance, and $p_i$ is the index of the antenna you activate in the $i$-th step.

If there are multiple solutions, you can print any of them.

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq a_1 < a_2 < \dots < a_N \leq 10^9$
• $0 \leq b_1 < b_2 < \dots < b_N \leq 10^9$
• $a_1, a_2, \dots, a_N, b_1, b_2, \dots, b_N$ are all distinct.
• All values in input are integers.