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);
$colors = [];
$add_color = True;
for ($i = 0; $i < $n; $i++) {
  $add_color = True;
  fscanf(STDIN, "%d", $num);
  for ($k = 0; $k < count($colors); $k++) {
  	if ($colors[$k] < $num) {
      $colors[$k] = $num;
      $add_color = False;
      break;
    }
  }
  if ($add_color) {
    $l = count($colors);
    $colors[$l] = $num;
  }
}
echo count($colors);