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: Accepted)

import java.io.*;
import java.util.*;

class Main {

    private static PrintWriter out;

    private static <T> void mprintln(T... ar) {
        for (T i : ar) {
            out.print(i + " ");
        }
        out.println();
    }

    public static void main(String[] args) throws FileNotFoundException {

        // Input from file
        // File inputFile = new File("JavaFile.txt");
        // File outputFile = new File("JavaOutputFile.txt");
        // FileReader fileReader = new FileReader(inputFile);
        // Here it ends

        MyScanner sc = new MyScanner();
        // MyScanner sc = new MyScanner(fileReader);

        out = new PrintWriter(new BufferedOutputStream(System.out)); // Output to console
        // out = new PrintWriter(new PrintStream(outputFile)); // Output to file

        getAns(sc);

        out.close();
    }

    /*
     *Don't use builtin function (Math.ceil)
     */

    static final long MOD = (long) (1e9 + 7);

    private static void getAns(MyScanner sc) {
        int n = sc.ni();
        int[] ar = sc.niArr0(n);

        ArrayList<Integer> list = new ArrayList<>();
        for (int in: ar) {
//            System.out.println(list);
            if (list.isEmpty() || list.get(list.size() - 1) >= in) {
                list.add(in);
                continue;
            }

            list.set(findLargestSmallerThanMe(in, list), in);
        }

        out.println(list.size());
    }

    private static int findLargestSmallerThanMe(final int key, final ArrayList<Integer> list) {
        int start = 0, end = list.size() - 1;

        while (start < end) {
            int mid = start + (end - start) / 2;
            if (list.get(mid) < key) end = mid;
            else start = mid + 1;
        }

        return end;
    }

    static class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        MyScanner(FileReader fileReader) {
            br = new BufferedReader(fileReader);
        }

        MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nn() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            String ans = "";
            try {
                ans = br.readLine();
            } catch (IOException ex) {
                ex.printStackTrace();
            }
            return ans;
        }

        char nc() {
            return nn().charAt(0);
        }

        int ni() {
            return Integer.parseInt(nn());
        }

        long nl() {
            return Long.parseLong(nn());
        }

        double nd() {
            return Double.parseDouble(nn());
        }

        int[] niArr0(int n) {
            int[] ar = new int[n];
            for (int i = 0; i < n; i++) {
                ar[i] = ni();
            }
            return ar;
        }

        int[] niArr1(int n) {
            int[] ar = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                ar[i] = ni();
            }
            return ar;
        }

        long[] nlArr0(int n) {
            long[] ar = new long[n];
            for (int i = 0; i < n; i++) {
                ar[i] = nl();
            }
            return ar;
        }

        long[] nlArr1(int n) {
            long[] ar = new long[n + 1];
            for (int i = 1; i <= n; i++) {
                ar[i] = nl();
            }
            return ar;
        }
    }
}