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

class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	void run() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] f = new int[n];
		int sz = 0;
		int[] a = new int[n];
		for (int i = 0; i < n; ++i) {
			a[i] = sc.nextInt();
			if (sz == 0) {
				f[sz] = a[0];
				++sz;
			} else {

				int ok = -1;
				int ng = sz;
				while (ng - ok > 1) {
					int middle = (ok + ng) / 2;
					if (f[middle] < a[i]) {
						ok = middle;
					} else {
						ng = middle;
					}
				}

				f[ok + 1] = a[i];
				if (ok + 1 == sz)
					++sz;
			}
		}
		
		System.out.println(sz);

	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}