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)

line = readlines.map(&:to_i)

N = line[0]

ans = []
for i in 1..N do
  if ans == [] then
    ans.push(line[i])
  else
    found = false
    j = (ans.length - 1) / 2
    min = 0
    max = ans.length
    while found == false do
      if ans[j] >= line[i] then
        min = j + 1
        j = (max + j) / 2
      elsif ans[j] < line[i] then  #can be colored j
        max = j
        j = (min + j) / 2
      end
      if min == max then
        found = true
      end
    end
    if min == -1 then
      ans.push(line[i])
    else
      ans[min] = line[i]
    end
  end
end
        
print ans.length