Greedily Increasing Subsequence

Source: Kattis

Version: Phuoc Hung OJ Extended

Problem Statement

Given a permutation $A=(a_1,\ldots,a_N)$ of $1,2,\ldots,N$, build its greedily increasing subsequence (GIS): set $g_1=a_1$, then repeatedly take the first later element that is strictly larger than the last chosen element. Stop when no such element remains. Print the GIS.

Input

The first line contains $N$. The second line contains the permutation $a_1,\ldots,a_N$.

Output

Print the GIS length on the first line and the GIS elements on the second line.

Subtasks

General constraints:

• $1 \le N \le 2\cdot10^5$.

• $A$ is a permutation of $1,2,\ldots,N$.

• Subtask 1 (20 points): $N \le 20$

• Subtask 2 (30 points): $N \le 5000$

• Subtask 3 (50 points): No additional constraints.

Examples

Input

7
2 3 1 5 4 7 6

Output

4
2 3 5 7

Explanation

Start with $2$. The first later value larger than $2$ is $3$, then $5$, then $7$. No later value exceeds $7$.