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)

class SegmentTree
  def initialize(n)
    @sz=1
    while @sz<n
      @sz*=2
    end
    @seg=Array.new(2*@sz-1){0}
    @root=0
    @nil=-1
  end

  attr_accessor :seg

  def max(a, b, i=@root, l=0, r=@sz)
    if b<=l or r<=a
      @nil
    elsif a<=l and r<=b
      @seg[i]
    else
      m=(r+l)/2
      vl=max(a, b, 2*i+1, l, m)
      vr=max(a, b, 2*i+2, m, r)
      [vl, vr].max
    end
  end

  def update(i, data)
    i+=@sz-1
    @seg[i]=data
    while i.nonzero?
      i=(i-1)/2
      @seg[i]=[@seg[2*i+1], @seg[2*i+2]].max
    end
  end

  def answer
    @seg[@root]
  end
end


n=gets.to_i
a=[]
n.times do |i|
  e=gets.to_i
  a<< [e, -i]
end

b=a.sort_by do |_a|
  [_a[0], _a[1]]
end

st=SegmentTree.new(n)
b.each do |_b|
  i=-_b[1]
  st.update(i, st.max(0, i+1)+1)
end

puts st.answer