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
# 入力
fscanf(STDIN, '%d', $n);
$a = [0];
for ($i = 1; $i <= $n; $i++) {
    $a[] = intval(trim(fgets(STDIN)));
}

$b = [-1];
$cnt = 1;
$min = -1;
for ($i = 1; $i <= $n; $i++) {
    if ($a[$i] <= $min) {
        $b[] = $a[$i];
        $cnt++;
        $min = $a[$i];
        continue;
    }
    foreach ($b as $j => $v) {
        if ($a[$i] > $b[$j]) {
            $b[$j] = $a[$i];
            if ($j === count($b) - 1) {
                $min = $a[$i];
            }
            break;
        }
    }
}
echo $cnt.PHP_EOL;
?>