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: Wrong Answer)

import java.util.Scanner;
import java.util.Arrays;

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

    for ( int i = 0; i < sequence.length; i++ ) {
      sequence[i] = sc.nextInt();
    }
    System.out.println(findLISLen(sequence));
  }

  public static int findLISLen(int[] sequence) {
      
    // lens[i] refers among all subsequences with len i
    // the index of smallest ending value of them
    int maxLen = 0, newL = 0;
    int[] lens = new int[sequence.length+1];

    for ( int i = 0; i < sequence.length; i++ ) {
        
        // binary search
        int lo = 1, hi = maxLen;
        while ( lo <= hi ) {
          int mid = lo+(hi-lo)/2;
          if ( sequence[lens[mid]] <= sequence[i] ) {
            lo = mid+1; 
          } else {
            hi = mid-1;
          }
        }

        newL = lo;
        lens[newL] = i;
        maxLen = Math.max(maxLen, newL);
    }
    return maxLen;
  }
  
}