Description:

Mr. Zstu and Mr. Hdu are taking a boring class , Mr. Zstu comes up with a problem to kill time, Mr. Hdu thinks it’s too easy, he solved it very quickly, what about you guys?

Here is the problem:

Give you two sequences L1,L2,...,Ln and R1,R2,...,Rn.

Your task is to find a longest subsequence v1,v2,...vm satisfies

v1≥1,vm≤n,vi<vi+1 .(for i from 1 to m - 1)

Lvi≥Lvi+1,Rvi≤Rvi+1(for i from 1 to m - 1)

If there are many longest subsequence satisfy the condition, output the sequence which has the smallest lexicographic order.

Input:

There are several test cases, each test case begins with an integer n.

1≤n≤50000

Both of the following two lines contain n integers describe the two sequences.

1≤Li,Ri≤109

Output:

For each test case ,output the an integer m indicates the length of the longest subsequence as described.

Output m integers in the next line.

Output m integers in the next line.

Sample Input:

5 5 4 3 2 1 6 7 8 9 10 2 1 2 3 4

Sample Output:

5 1 2 3 4 5 1 1

Source:

Submit