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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$n = intval(fgets(STDIN));
$min = 10**18;
$c = 0;
for($i = 0; $i < $n; $i++){
  $A[] = 10**10-intval(fgets(STDIN));
}
echo lis($A);

function lis($A){
    $dp = array_fill(0, count($A)+1, PHP_INT_MAX);
    $dp[0] = 0;
    $longest = 0;
    foreach($A as $a){
        $b = lower_bound($dp, $a+1);
        $dp[$b] = $a;
        $longest = max($longest, $b);
    }
    return $longest;
}
function lower_bound($array, $key){
  $min = -1;
  $max = count($array);
  while($max - $min > 1){
    $c = intdiv($min + $max, 2);
    if($array[$c] >= $key){
      $max = $c;
    }else{
      $min = $c;
    }
  }
  return $max;
}