Longest Increasing Subsequence

Background

Special for beginners, ^_^

Problem Description

Consider a sequence composed of $n$ distinct integers, denoted $b_1, b_2, \dots, b_n$ with $b_i \neq b_j$ ($i \neq j$). If there exist indices $i_1 < i_2 < i_3 < \dots < i_e$ such that $b_{i_1} < b_{i_2} < \dots < b_{i_e}$, then this is called an increasing subsequence of length $e$.

Given the original sequence, find its longest increasing subsequence.

For example, 13, 7, 9, 16, 38, 24, 37, 18, 44, 19, 21, 22, 63, 15.

In this example, 13, 16, 18, 19, 21, 22, 63 is an increasing subsequence of length 7, and at the same time 7, 9, 16, 18, 19, 21, 22, 63 is an increasing subsequence of length 8.

Input Format

One line containing several positive integers; the count is less than 100, and each value is less than 50000.

Output Format

Output two lines.

The first line outputs an integer $e$.

The second line outputs $e$ integers, the longest increasing subsequence.

Sample Input 1

300 250 275 252 200 138 245

Sample Output 1

2
250 275 

Constraints

1s, 1024KiB for each test case.