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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
  
while ($line = fgets(STDIN)) {
   $stdin[] = trim($line);
}
#$v2 = str_split($stdin[0]);
#$v2 = explode(" ", $stdin[0]);

#var_dump($stdin);

unset($stdin[0]);

$counter = 0;
foreach($stdin as $k => $v){
  
  if($k == count($stdin)){ break; }
  
  if($v > $stdin[$k + 1] || $v == $stdin[$k + 1]){
    #var_dump($v);
    $counter++;
  }else{
    $maxcounter[] = $counter;
    $counter = 0;
  }
}

if(!isset($maxcounter)){
  $ans = count($stdin) + 1;
}else{
  $ans = max($maxcounter) + 1;
}

echo $ans . PHP_EOL;