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: Accepted)

N = gets.chomp.to_i
AS = []
N.times { AS.push(gets.chomp.to_i) }

arr = [AS[0]]
arr2 = [[AS[0]]]

1.upto(N - 1) do |i|
  if AS[i] <= arr[0]
    arr.unshift(AS[i])
    arr2.unshift([AS[i]])
    next
  end
  if AS[i] > arr[-1]
    arr[-1] = AS[i]
    arr2[-1].push(AS[i])
    next
  end
  a = 0
  b = arr.size - 1
  while a < b
    c = (a + b) / 2
    if arr[c + 1] < AS[i]
      a = [c, a + 1].max 
    elsif arr[c] >= AS[i]
      b = [c, b - 1].min
    else
      a = b = c
    end
  end
  arr[c] = AS[i]
  arr2[c].push(AS[i])
end

puts arr.size