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 (7.4.4) (judge verdict: Accepted)

<?php
list($n) = ints();
for ($i = 0; $i < $n; ++$i) list($a[]) = ints();
// 同じ色で塗れるマスをグループ分けした時のグループごとの末尾の値を格納
// この数より大きい数字であればこのグループに入れられる
$ends = [$a[0]];
for ($i = 1; $i < $n; ++$i) {
    // 二分探索で入れられるグループのうち末尾の値が最大のものを探す
    // endsは常にソート済（降順）
    $l = count($ends);
    $ok = $l;
    $ng = -1;
    while (abs($ok - $ng) > 1) {
        $mid = intdiv($ok + $ng, 2);
        if ($ends[$mid] < $a[$i]) $ok = $mid;
        else $ng = $mid;
    }
    // 見つからない場合はok=lなので要素が追加される
    $ends[$ok] = $a[$i];
}
echo count($ends);
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}