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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

function Main(input) {
  input=input.split("\n");
  if(input[input.length-1]===''){
    input.pop();
  }
  const N=input[0]-0;
  var colors=[];
  var temp;
  var min,max,mid;
  for(var i=1;i<input.length;i++){
    temp=input[i]-0;
    if(colors.length===0){
      colors.push(temp);
      continue;
    }
    if(temp<=colors[0]){
      colors.unshift(temp);
      continue;
    }
    if(temp>colors[colors.length-1]){
      colors[colors.length-1]=temp;
      continue;
    }
    min=0;
    max=colors.length-1;
    while(max-min>1){
      mid=Math.floor((max+min)/2);
      if(colors[mid]<temp){
        min=mid;
      }else{
        max=mid;
      }
    }
    colors[min]=temp;
  }
  console.log(colors.length);
}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));