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
fscanf(STDIN, "%d", $n);
$l = [];
for ($i=0; $i < $n; $i++) {
    fscanf(STDIN, "%d", $a);
    if (count($l) === 0) {
        $l[] = $a;
    } else {
        list($max, $index) = get_smaller_max($a, $l);
        if ($max === -1) {
            $l[] = $a;
        } else {
            $l[$index] = $a;
        }
    }
}
echo count($l);

function get_smaller_max($a, $l) {
    $max = -1; $index = -1;
    for ($i=0; $i < count($l); $i++) {
        if ($l[$i] < $a && $l[$i] > $max) {
            $max = $l[$i];
            $index = $i;
        }
    }
    return [$max, $index];
}
?>