Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

def inpf() a=gets.chomp.split(" ").map(&:to_f)end

def inps() a=gets.chomp.split(" ")end

def copy(a) Marshal.load(Marshal.dump(a)) end

def kaijo(n,r = 10**9+7)(n < 2)? 1 : (2..n).inject{|memo,u|memo=(memo*u)%r} end

def na(n,d=0) Array.new(n,d)end

def na2(n,m,d=0) Array.new(n){Array.new(m,d)}end

def na3(n,m,l,d=0) Array.new(n){Array.new(m){Array.new(l,d)}}end

def inp() a=gets.chomp.split(" ").map(&:to_i)end

def r_up(a, b) (a+b-1)/b end

def b_ser(bot, top, a, target, u_r_f = nil, mm = nil)
  mid = (bot + top)/2
  if(a[mid] == target)
    if(u_r_f == nil)
      return mid
    else
      return mid if(bot == mid)
      return b_ser(bot, mid, a, target, u_r_f, mid)
    end
  end
  if(bot == mid)
    return nil if(u_r_f == nil)
    return mid + ((a[mid] < target)? 1 : 0)
  end
  return (a[mid] > target)? b_ser(bot, mid, a, target, u_r_f, mm) : b_ser(mid, top, a, target, u_r_f, mm)
end
n = inp[0]
it = []
n.times do
  it << inp[0]
end
len = [it.shift]
it.each do |d|
  ind = nil
  if(len.size == ind = b_ser(0,len.size,len,d-1,true))
    it[ind] = d
  else
    len.push(d)
  end
end
p len.size