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: Time Limit Exceeded)

<?php
fscanf(STDIN, "%d", $n);
$iro=array();
for($i=0; $i<$n; $i++){
  fscanf(STDIN, "%d", $a);
  //初期値
  $key=0;
  $change=0;
  
  foreach($iro as $k=>$v){
    if($v<$a){
      //色リストより大きい(key保持)
      $key=$k;
      $change=1;
    }else{
      //色リストより小さい
      break;
    }
  }
  //色リスト追加・更新
  array_splice($iro, $key, $change, $a);
}
echo count($iro);