Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Mike and distribution

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMike has always been thinking about the harshness of social inequality. He's so obsessed with it that sometimes it even affects him while solving problems. At the moment, Mike has two sequences of positive integers *A* = [*a*_{1}, *a*_{2}, ..., *a*_{n}] and *B* = [*b*_{1}, *b*_{2}, ..., *b*_{n}] of length *n* each which he uses to ask people some quite peculiar questions.

To test you on how good are you at spotting inequality in life, he wants you to find an "unfair" subset of the original sequence. To be more precise, he wants you to select *k* numbers *P* = [*p*_{1}, *p*_{2}, ..., *p*_{k}] such that 1 ≤ *p*_{i} ≤ *n* for 1 ≤ *i* ≤ *k* and elements in *P* are distinct. Sequence *P* will represent indices of elements that you'll select from both sequences. He calls such a subset *P* "unfair" if and only if the following conditions are satisfied: 2·(*a*_{p1} + ... + *a*_{pk}) is greater than the sum of all elements from sequence *A*, and 2·(*b*_{p1} + ... + *b*_{pk}) is greater than the sum of all elements from the sequence *B*. Also, *k* should be smaller or equal to because it will be to easy to find sequence *P* if he allowed you to select too many elements!

Mike guarantees you that a solution will always exist given the conditions described above, so please help him satisfy his curiosity!

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{5}) — the number of elements in the sequences.

On the second line there are *n* space-separated integers *a*_{1}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{9}) — elements of sequence *A*.

On the third line there are also *n* space-separated integers *b*_{1}, ..., *b*_{n} (1 ≤ *b*_{i} ≤ 10^{9}) — elements of sequence *B*.

Output

On the first line output an integer *k* which represents the size of the found subset. *k* should be less or equal to .

On the next line print *k* integers *p*_{1}, *p*_{2}, ..., *p*_{k} (1 ≤ *p*_{i} ≤ *n*) — the elements of sequence *P*. You can print the numbers in any order you want. Elements in sequence *P* should be distinct.

Example

Input

5

8 7 4 8 3

4 2 5 3 7

Output

3

1 4 5

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/26/2017 21:13:06 (c3).

Desktop version, switch to mobile version.

User lists

Name |
---|