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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

const maxn = trunc(1e5);
var n,re,k,x,count,i:longint;
    d:array[1..maxn] of integer;
    a:array[1..maxn] of longint;

begin
	readln(n);
	fillchar(d,sizeof(d),0);
	for i:=1 to n do readln(a[i]);
	count:=1; x:=a[1]; k:=1; re:=0; d[1]:=1;
	repeat
	  for i:=k to n do
	    if (d[i] = 0) and (a[i] > x) then 
	      begin
	        inc(count); d[i]:=1;
	      end;
	  for i:=2 to n do
	    if d[i] = 0 then
	      begin
	        x:=a[i]; d[i]:=1; inc(count); k:=i + 1;
	        if count = n then inc(re);
	        break;
	      end;
	  inc(re);
	until count = n;
	write(re);
end.