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: Wrong Answer)

while true
  n = gets.to_i
  break if n == 0
  as = []
  n.times do 
    as.push(gets.to_i)
  end
  length = 1
  top = -1
  second_top = 0
  as.each do |a|
    if length == 1
      old_top = top
      top = a
      next if old_top < 0 || old_top >= a
      length += 1
      next
    end
    if top < a
      length += 1
      top = a
      next
    end
    if second_top < a
      top = a
      next
    end
  end
  puts length
end