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)

def lower_bound(a, l, r, v)
	m = l
	until m == r
		l, r = a[m] < v ? [m, r] : [l, m]
		m = l + (r-l+1)/2
	end
	return m
end

N  = gets.to_i
probes = []

N.times{
	a = gets.to_i
	i = lower_bound(probes, 0, probes.length, a)
	if i == 0
		probes.unshift(a)
	else
		probes[i-1] = a
	end
}

p probes.length