Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in OCaml (judge verdict: Accepted)

let lower_bound (a : int array) first last v =
  let rec doit len first =
    if len = 0 then first
    else
      let half = len / 2 in
      let mid = first + half in
      if a.(mid) < v then doit (len - half - 1) (mid + 1)
      else doit half first in
  doit (last - first + 1) first

let () =
  let n = read_int () in
  let dp = Array.make (n + 1) max_int in
  for _ = 0 to n - 1 do
    let a = read_int () in
    dp.(lower_bound dp 0 n a) <- a
  done;
  lower_bound dp 0 n max_int |> Printf.printf "%d\n"