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)

N = gets.to_i
arr = N.times.map{ gets.to_i }
stack = []
counter = 0
arr.each do |i|
  if !stack.empty? && stack.last >= i
    if stack[stack.count - 2] < stack[stack.count - 1]
      flag = false
      while !stack.empty?
        if stack[stack.count - 2] < stack[stack.count - 1]
          flag = true
          stack.pop
        else
          break
        end
      end
      stack.pop
      counter += 1 if flag
    end
  end
  stack.push(i)
end

while !stack.empty?
  i = stack.count
  if stack[i - 2] < stack[i - 1]
    flag = false
    while !stack.empty?
      if stack.count >= 2 && stack[stack.count - 2] < stack[stack.count - 1]
        flag = true
        stack.pop
      else
        break
      end
    end
    stack.pop
    counter += 1 if flag
  else
    stack.pop
    counter += 1
  end
end

puts counter