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: Time Limit Exceeded)

<?php
$n = int();
$maxArray = [10**10];

$count = 0;
for($i = 0; $i < $n; $i++){
  $a = int();
  $b = bsl($maxArray, $a-1);
  if($b == -1){
    array_unshift($maxArray, $a);
    $count++;
  }else{
    $maxArray[$b] = $a;
  }
}
echo $count;
function bsl($nums, $target) {
    $size = count($nums);
    $min = 0; 
    $max = $size - 1;
    while(true){
        $center = floor(($min + $max) / 2);
        $centerValue = $nums[$center];
        if($target == $centerValue){
            return $center;
        }elseif($target > $centerValue){
            $min = $center + 1;
        }else{
            $max = $center;
        }
        if($min == $max){
            $center = floor(($min + $max) / 2);
            $centerValue = $nums[$center];
            if($centerValue == $target){
                return $center;
            }elseif($centerValue < $target){
                return $center;
            }else{
                return $center-1;
            }
        }
    }
}
function str(){
  return trim(fgets(STDIN));
}
function ints(){
  return array_map("intval", explode(" ", trim(fgets(STDIN))));
}
function int(){
  return intval(trim(fgets(STDIN)));
}
function o(...$val){
    if(count($val)==1)$val = array_shift($val);
    $trace = debug_backtrace();
    echo $trace[0]['line'].")";
    if(is_array($val)){
        if(count($val) == 0){
            echo "empty array";
        }elseif(!is_array(current($val))){
            echo "array:";
            echo implode(" ", $val)."\n";
        }else{
            echo "array:array\n";
            foreach($val as $row){
                echo implode(" ", $row)."\n";
            }
        }
    }else{
        echo $val."\n";
    }
}