Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in JAVA (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import static java.lang.System.*;
import static java.lang.Math.*;

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

    int[] A = new int[n];
    int[] L = new int[n];

    for (int i = 0; i < n; i++) {
      A[i] = sc.nextInt();
    }
    sc.close();

    L[0] = A[0];
    int length = 1;

    for (int i = 1; i < n; i++) {
      if(L[length-1] < A[i]){
        L[length++] = A[i];
      }else{
        int index = ~Arrays.binarySearch(L, 0, length, A[i]);
        if (index < 0) index = ~index;
        L[index] = A[i];
      }
    }

    out.println(length);
	}
}