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)

a = []
l = []
gets.to_i.times do
  a << gets.to_i
end

l[0] = a[0]
length = 1

(1...a.size).each do |i|
  if l[length-1] < a[i]
    l[length] = a[i]
    length += 1
  else
    j = (0...l.size).bsearch { |k| a[i] <= l[k] }
    l[j] = a[i]
  end
end
puts length