Boring Class

Time Limit: 6000/3000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)


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 ${L_1,L_2,...,L_n}$ and ${R_1,R_2,...,R_n}$.
Your task is to find a longest subsequence ${v_1,v_2,...v_m}$ satisfies
$v_1 \geq 1$,$v_m \leq n$,$v_i < v_{i+1}$ .(for i from 1 to m - 1)
$L_{v_i} \geq L_{v_{i+1}}$,$R_{v_i} \leq R_{v_{i+1}}$(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.


There are several test cases, each test case begins with an integer n.
$1 \leq n \leq 50000$
Both of the following two lines contain n integers describe the two sequences.
$1 \leq L_i,R_i \leq 10^9$


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.

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




2015 Multi-University Training Contest 3