Problem B
Greedily Increasing Subsequence

Given a permutation $A=(a_1,a_2,\dots ,a_N)$ of the integers $1,2,\dots ,N$, we define the greedily increasing subsequence (GIS) in the following way.

Let $g_1=a_1$. For every $i>1$, let $g_i$ be the leftmost integer in $A$ that is strictly larger than $g_{i-1}$. If there for a given $i$ is no such integer, we say that the GIS of the sequence is the sequence $(g_1,g_2,...,g_{i-1})$.

Your task is to, given a permutation $A$, compute the GIS of $A$.

Input

The first line of input contains an integer $1\le N\le {10}^6$, the number of elements of the permutation $A$. The next line contains $N$ distinct integers between $1$ and $N$, the elements $a_1,\dots ,a_N$ of the permutation $A$.

Output

First, output a line containing the length $l$ of the GIS of $A$. Then, output $l$ integers, containing (in order) the elements of the GIS.

Explanation of sample 1

In this case, we have the permutation $2,3,1,5,4,7,6$. First, we have $g_1=2$. The leftmost integer larger than $2$ is $3$, so $g_2=3$. The leftmost integer larger than $3$ is $5$ ($1$ is too small), so $g_3=5$. The leftmost integer larger than $5$ is $7$, so $g_4=7$. Finally, there is no integer larger than $7$. Thus, the GIS of $2,3,1,5,4,7,6$ is $2,3,5,7$.

7
2 3 1 5 4 7 6

4
2 3 5 7

5
1 2 3 4 5

5
1 2 3 4 5

5
5 4 3 2 1

1
5