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)

eval'K,X,Y='+`dd`.split*?,;x,y,*s=X.abs,Y.abs;d=x+y;x,y=y,x if f=x>y;K%2-d%2<0&&(p -1;exit);n=(d-1)/K+1;n+=d<K ? 1 :(d-n*K)%2;a=n<2 ?x:(d-n*K)/2;b=K-a.abs;d%2-d/K>0&&(s=[[0,-K]];a=b=(d-K)/2);n.times{s<<[a,b];t=[x-a,K].min;a+=t;b+=K-t};p s.size;s.each{|a,b|f&&(a,b=b,a);puts [a*(X<=>0.1),b*(Y<=>0.1)]*?\s}