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 Ruby (judge verdict: Accepted)

n = gets.to_i
a = (0..n).map {|i| i == 0 ? -1 : Float::INFINITY }
n.times do
  x  = gets.to_i
  i = (0..n).bsearch {|i| a[i] >= x } - 1
  a[i + 1] = x
end
n.downto(0) do |i|
  if a[i] != Float::INFINITY
    p i
    break
  end
end