Longest Ordered Subsequence

A numeric sequence $a_i$ is called ordered if $a_1 \le a_2 \le \dots \le a_N$. For a given sequence $(a_1, a_2, \dots, a_N)$, a subsequence is any sequence $(a_{i_1}, a_{i_2}, \dots, a_{i_K})$ with $1 \le i_1 < i_2 < \dots < i_K \le N$.

For example, the sequence $(1, 7, 3, 5, 9, 4, 8)$ has ordered subsequences such as $(1, 7)$ and $(3, 4, 8)$. All of its longest ordered subsequences have length 4, for example $(1, 3, 5, 8)$.

Given the sequence, find the length of its longest ordered subsequence.

The first line contains the length of the sequence $N$ ($1 \le N \le 1000$). The second line contains $N$ integers — the elements of the sequence, each in the range from $0$ to $10000$, separated by spaces.

Print a single integer: the length of the longest ordered subsequence of the given sequence.