You are given two sequences of integer numbers. Write a program to determine their common increasing subsequence of maximal possible length.
Sequence S
1 , S
2 , . . . , S
N of length N is called an increasing subsequence of a sequence A
1 , A
2 , . . . , A
M of length M if there exist 1 <= i
1 < i
2 < . . . < i
N <= M such that S
j = A
ij for all 1 <= j <= N , and S
j < S
j+1 for all 1 <= j < N .
Each sequence is described with M --- its length (1 <= M <= 500) and M integer numbers A
i (-2
31 <= A
i < 2
31 ) --- the sequence itself.
On the first line of the output file print L --- the length of the greatest common increasing subsequence of both sequences. On the second line print the subsequence itself. If there are several possible answers, output any of them.