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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.util.Scanner;

 class Main {


    private static int floorSearch(int[] dp, int l, int r, int x){
        int mid=1;
       // int floor=0;
        if(x>=dp[r])
            return r;
        while(l<=r){
            mid=(r+l)/2;
            if(dp[mid]==x)
                return mid;
            else{
                if (mid >0 && dp[mid-1] <= x && x < dp[mid])
                    return mid-1;
                if(x< dp[mid]){
                    r=mid-1;
                }
                else{
                    l=mid+1;
                }
            }
        }
        return mid;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] a =new int[n];

        for(int i=0;i<n;i++){
            a[i]=in.nextInt();
        }
        int[] dp =new int[n];
        dp[0]=a[0];
        int len=1;

        for(int i=1;i<n;i++){
            if(a[i]>dp[0])
                dp[0]=a[i];
            else{
                if(a[i]<=dp[len-1]){
                    dp[len++]=a[i];
                }
                else{
                    dp[floorSearch(dp, 0, len-1, a[i])]=a[i];
                }
            }
//            for(int j=0;j<len;j++)
//                System.out.print(" " + dp[j]);
//            System.out.println("\n");
        }
        System.out.println(len);

    }
}