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: Wrong Answer)

<?php
$n = intval(fgets(STDIN));
$maxLen = 0;
$currentLen = 0;
$currentNum = 10**10;
for($i = 0; $i < $n; $i++){
  $a = intval(fgets(STDIN));
  if($a <= $currentNum){
    $currentNum = $a;
    $currentLen++;
    $maxLen = max($maxLen, $currentLen);
  }else{
    $currentLen = 1;
    $currentNum = 10**10;
  }
}
echo $maxLen;