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: Runtime Error)

n = gets.to_i
a = []
n.times{ a << gets.to_i }
dp =  Array.new
dp << -1
n.times do |i|
  if dp.last < a[i]
    dp << a[i]
  else
    left = 0
    right = dp.size
    mid = 0
    while left <= right
      mid = (left + right)/2
      if a[i] >= dp[mid]
        left = mid + 1
      else
        right = mid - 1
      end
    end
    if dp[right] < a[i] && dp[right+1] > a[i]
      dp[right+1] = a[i]
    end
  end
end
p dp.size - 1